Y&r<W* 

I          W..W«TO 


OP  THE 


JVo. 

Division 
Range 
Shelf. 
Received    *#.*• 


HEAT 

AS    A    SOURCE    OF    POWER; 

WITH  APPLICATIONS  OF  GENERAL  PRINCIPLES 


CONSTRUCTION  OP  STEAM  GENERATORS. 


AN    INTRODUCTION    TO    THE    STUDY    OF 


HEAT-ENGINES. 


BY 

WILLIAM  P.    TKOWBKIDGE, 

HIGGIH  PROFESSOR   OF  DYNAMIC  ENGINEERING  IN  THE  SHEFFIELD  SCIENTIFIC  SCHOOL  OF 

YALE   COLLEGE. 

L 1 1*  R  A  R  Y 

UNIVERSITY   OF 


CALIFORNIA. 


NEW  YORK: 
JOHN  WILEY  &  SON 

15  ASTOB,  PLACE. 


Entered  according  to  Act  of  Congress,  in  the  year  1874,  by 

JOHN    WILEY    &    SON, 
In  the  Office  of  the  Librarian  of  Congress,  at  Washington,  D.  C. 


JOHN  F.  TROW  &  SON, 

PRINTERS  AND  BOOKBINDERS, 

205-213  East  \'2.th  St., 

NEW   YORK. 


CONTENTS. 


CHAPTER  I. 

• 

Heat. 

PAEAGEAPH 

Dynamic  Theory  of  Heat 1 

Phenomena  connected  with  Heat 16 

Unit  of  Heat 42 

Fundamental  Law  of  Thermo-dynamics ." 44 

Specific  Heats 52 

Aclion  of  Heat  on  Bodies  in  Nature 57 

Coefficient  of  Expansion 69 

Liquefaction,  Melting,  or  Fusion 71 

Latent  Heat  of  Fluidity 75 

Expansion  of  Liquids 76 

Expansion  of  Gases • 77 

Law  of  Mariotte  and  Gay-Lussac 79 

Absolute  Temperature 82 

Problems  relating  to  Pressures,  Volumes,  and  Temperatures 86 

Poisson's  Formulae 91 

Vapors 92 

Complete  Vaporization 98 

Boiling-point 100 

Superheated  Vapor 107 

Spheroidal  State 108 

Hu*nid  Vapor 109 

Expansion  of  Dry  Saturated  Steam 110 

Specific  Heats  of  Gases  and  Vapors Ill 

Theoretical  Verification  of  the  Dynamic  Equivalent  of  Heat 114 

Elastic  Force  of  Vapors 116 

Reguault's  Experiments  and  Tables 120 

Latent  Heat 123 

Latent  Heat  of  Fusion 124 

Latent  Heat  of  Vaporization 125 

Total  Heat  of  Vaporization 127 

Factor  of  Evaporation 129 

Total  Heat  of  Superheated  Steam 130 

Zeuner's  Tables 132 

Total  Heat  in  Wet  Steam 133 

Density  of  Gases  and  Vapors 135 


IV  CONTENTS. 

CHAPTEE  II. 
Combustion. 

PABAGBAPH 

Combustion 143 

Inflammation 144 

Ignition 145 

Spontaneous  Combustion 151 

Ordinary  Combustion 152 

Composition  of  Atmospheric  Air 156 

Products  of  Combustion .* 156 

Heat  Evolved  in  Chemical  Combination 163 

CHAPTER  III.  ' 
Fuel. 

Combustion  of  Illuminating  Gas 167 

Natural  Solid  Combustibles 168 

Artificial  Solid  Combustibles 170 

Properties  of  Anthracite 171 

Bituminous  Coals 172 

Lignites 173 

Peat 174 

Wood 175 

Wood  Charcoal 176 

Coke 177 

Kind  of  Fuel  to  be  used..                                                             178 


CHAPTER  IY. 
The  Transfer  of  Heat. 

General  Considerations 181 

Transfer  of  Heat  by  Eadiation 183 

Action  of  Bodies  on  Radiant  Heat 192 

Transfer  of  Heat  by  Contact 196 

Conduction  of  Heat 201 

Conduction  by  Gases , 203 

Temperature  accompanying  Combustion 204 

Transfer  of  Heat  in  Steam-boilers. .  200* 


CONTENTS. 


CHAPTER  Y. 
Steam  Generators. 

PABAOBAPH 

General  Considerations 207 

Conditions  to  be  fulfilled 208 

Forms  of  Boilers 210 

Types  of  Boilers 211 

Plain  Cylinder  Boiler * 212 

Description  of  Parts  and  Appendages 212 

Cylinder-Flue  Boiler 214 

Cornish  Boiler. 215 

Cylinder-Tubular  Boiler 216 

Marine  Tubular  Boiler 220 

Marine  Water-Tube  Boiler 221 

Locomotive  Boiler 222 

Fire-Engine  Boiler 224 

Sectional  Boilers...  226 


CHAPTER  YL 
The  Construction  of  Steam  Generators. 

Proportion  of  Parts 233 

Chimneys. 234 

Grate-Surf  ace 235 

Heating-Surface , 236 

Causes  which  affect  the  Efficiency  of  Evaporation 240 

Proportion  of  Water-room  and  Steam-room 243 

Priming 244 

Proportions  of  Furnace 245 

Actual  Dimensions 246 

Efficiency  of  Steam  Generators 247 

Horse-Power  of  Boilers 248 

Kinds  and  Quality  of  Materials  used  in  Construction 249 

Strength  of  Materials  used 251 

Theory  of  Stress  in  Boilers 252 

Joints 253 

Resistance  of  Flues  to  Collapse 254 

Stays 255 

Supply  of  Feed-water 256 

CHAPTER  VII. 
Boiler  Explosions. 

Rate  of  Increase  of  Pressure 258 

Safety-valves 259 

Sudden  Evolution  of  Steam. . ,  261 


VI  CONTENTS. 


APPENDIX. 

Laws  of  Mariotte  and  Gay-Lussac. 

Formulae  for  the  Flow  of  Gases  and  Vapors  through  Orifices. 


.TABLES. 

I.  Specific  Heats. 
II.  Linear  Expansions  of  Solids. 

III.  Melting-points  of  Substances. 

IV.  Latent  Heats  of  Fusion. 
V.  Expansion  of  Water. 

VI.  Cubical  Expansions. 

VII.  Values  of  Constants  in  Formula  of  Mariotte  and  Gay-Lussac 
VIII.  Boiling-points. 

IX.  Specific  Heats  at  different  Temperatures. 
X.  Specific  Heats  of  Gases. 
XI.  Temperatures  of  Saturated  Vapors  of  Water,  Alcohol,  and  Ether,  at 

different  Pressures. 
XII. .  Comparison  of  Results  of  Formulae. 

XIII.  Temperatures  and  Pressures  of  Steam — Regnault's  Table. 

XIV.  Ditto  from  Fairbairn's  Work. 

XV.  Zeuner's  Tables  of  Latent  Heats,  etc. 
XVI.  Relative  Densities. 
XVII.  Specific  Densities. 

XVIII.  Chemical  Formulas  and  Products  of  Combustion. 
XIX.  Products  of  Combustion  of  1  Ib.  of  given  Substances. 
XX.  Products  of  Combustion  by  Volume. 
XXI.  Heat  evolved  by  Combustion  of  different  Substances. 
XXII.   Composition  of  Illuminating  Gas. 

XXIII.  Combustion  of  Illuminating  Gas. 

XXIV.  Composition,  Calorific  Power,  and  Products  of  Combustion  of  differ- 

ent Substances. 

XXV.  Quantity  of  Watery  Vapor  in  Atmosphere  at  different  Temperatures. 
XXVI.  Relative  Conductivities. 
XXVII.  Quantities  of  Heat  transmitted  by  Conduction  in  a  given  Time,  for 

different  Substances. 
XXVIII.  Dimensions  of  Boilers  of  various   Types  suitable  for  evaporating 

given  Quantities  of  Water. 
XXIX.  Heights  of  Chimneys. 

XXX.  Quantities  of  Steam  required  in  Non- condensing  Engines  for  one 
H.  P.  per  Hour. 


JLJ  1   i) 


UNIVERSITY   OF 

GALIFORJS 


PREFACE. 


THE  employment  of  heat  as  a  source  of  energy,  or  power,  is 
accomplished  by  a  succession  of  processes  which  depend  for 
their  explanation  on  separate  branches  of  applied  science,  and 
practically  involve  the  use  of  different  forms  of  apparatus,  and 
the  applications  of  different  principles  of  mechanical  construc- 
tion. 

The  evolution  of  heat  by  combustion,  its  transfer  to  the 
bodies  through  which  it  acts,  the  changes  which  these  bodies 
undergo  when  subjected  to  changes  of  heat,  and  the  perform- 
ance of  work  by  expansion,  through  the  medium  of  machines, 
mark  successive  steps  which  can  be  rationally  and  properly  ex- 
plained only  by  reference  to  the  various  sciences  of  chemistry, 
physics,  dynamics,  and  mechanism,  on  which  they  respectively 
depend. 

The  most  intricate  and  complicated  of  these  processes  are 
those  which  accompany  the  development  of  heat,  and  which 
depend  on  the  relations  of  heat  to  chemistry,  and  to  the  physi- 
cal constitution  of  bodies.  A  thorough  knowledge  of  these 
relations,  or  laws,  is  of  primary  importance  in  all  economical 
questions  connected  with  the  use  of  this  agent  as  a  source  of 
power. 

The  dynamic  theory  of  heat  has  furnished,  through  investi- 
gations which  have  been  to  a  certain  extent  purely  theoretical 
and  mathematical,  solutions  of  the  principal  problems  connect- 
ed with  the  work  of  -expansion  of  gases  and  vapors ;  and  these 
solutions,  as  well  as  those  connected  with  mechanism,  partake 
of  the  exactitude  and  certainty  which  belong  to  mathemati- 
cal science.  The  principal  laws  connected  with  the  develop- 
ment of  heat,  and  the  physical  properties  exhibited  by  bodies 


viii  PREFACE. 

under  its  varying  influences,  have,  on  the  other  hand,  been 
discovered  mainly  through  experimental  researches,  and  the 
mathematical  expressions  of  these  laws  are  generally  simple 
algebraic  formulae,  which  have  been  found  to  accord  with  the 
results  of  such  investigations. 

These  elementary  principles  constitute  the  real  basis  of  the 
science  of  heat,  in  its  chemical  as  well  as  its  dynamic  relations, 
and  a  thorough  comprehension  of  them  is  necessarily  the  first 
step  to  be  taken  in  the  study  of  heat-engines. 

The  sfeam-engine  being  the  principal  heat-engine  in  use  at 
the  present  day,  prominence  must  be  given  to  the  study  of  the 
steam  generator,  as  the  apparatus  through  which  all  processes 
preliminary  to  the  actual  use  of  steam  are  accomplished. 

In  an  economical  point  of  view,  a  thorough  knowledge  of 
proper  forms  of  construction  and  of  proper  principles  of  man- 
agement of  this  apparatus,  is  of  no  less  importance  than  a 
knowledge  of  the  laws  of  expansion,  and  of  the  mechanisms  by 
which  the  heat  of  steam  is  utilized.  There  is,  perhaps,  even 
greater  need  of  the  dissemination  of  correct  useful  knowl- 
edge in  regard  to  the  construction  and  functions  of  the  steam 
generator,  than  of  the  mechanism  of  engines,  because  the 
construction  and  use  of  the  generator  are  more  subject  to  the 
uncertainties  of  personal  judgment  and  discretion ;  and  igno- 
rance of  elementary  principles  in  its  use  is  more  apt  to  cause 
waste. 

The  object  of  this  work,  as  an  introduction  to  the  study  of 
heat-engines,  is  simply  to  arrange  and  classify  the  elementary 
principles  in  such  a  way  that  they  may  be  accessible  to  the 
student^  unconnected  with  irrelevant  matter;  and  in  such  forms 
as  shall  lead  naturally  to  the  succeeding  steps — the  study  of 
the  principles  and  mechanism  of  engines. 

Any  work  of  this  character,  on  the  subject  of  heat  in  any  oi 
its  relations,  must  necessarily  be  a  reproduction,  to  a  great  ex- 
tent, of  what  in  various  forms  has  been  published  before ;  but 
the  facts  and  principles  which  I  have  endeavored  to  arrange, 
are  usually  found  scattered  through  text-books,  in  connection 


PREFACE.  ix 

with  other  subjects,  and  often  without  reference  to  technical 
applications. 

I  have  endeavored  to  mention,  as  far  as  practicable,  the 
various  sources  of  information  of  which  I  have  made  use  ;  and 
desire  to  express  my  indebtedness  to  the  authors  of  the  works 
consulted. 

SHEFFIELD  SCIENTIFIC  SCHOOL  OF  YALE  COLLEGE, 
January  8,  1874. 


JL  1  i>  A 

UNIVERSITY   OF 

CALIFOLiXlA. 

\^rrr  —r~~~ 

HEAT. 


OHAPTEE   I. 

HEAT. 

1.  Dynamic  Theory  of  Heat. — The  phenomena  connected 
with  Heat  are  so  common  and  universal,  so  intimately  related  to 
the  changes  in  constitution  and  form,  of  the  elements  which 
make  up  the  material  universe,  and  so  essential  to  the  existence 
of  animal  and  vegetable  life,  as  to  render  this  one  of  the  most 
important  and  varied  in  its  influences  of  all  the  physical  agents. 

2.  In  its  relation  to  animal  and  vegetable  life,  it  may  be  said 
to  be  the  main  support  of  vitality;  while,  as  a  source  of  energy, 
it  exists  in  all  bodies  as  a  living  force  in  the  literal  or  scientific, 
as  well  as  the  figurative,  sense  of  this  term. 

3.  The  employment  of  this  agent  as  a  source  of  artificial 
power  has  given  rise  to  investigations  by  scientific  men  during 
the  last  half  century,  which  have  become  historical,  and  which 
have  gradually  led  to  the  discovery  of  its  true  nature,  or  at  least 
to  a  universally  accepted  theory  regarding  it ;  and  it  may  be 
said,  that  while  differences  of  opinion  exist  concerning  the  pre- 
cise nature  of  molecular  motions,  the  essential  principles  of 
the  Dynamic  Theory  of  Heat  have  become  as  well  established 
as  any  other  known  or  accepted  law  of  physics. 

4.  In  explaining  this  theory,  heat  has  been  defined  to  be  a 
mode  of  motion  •  a  definition  which  suggests  appropriately  the 
idea  that  it  has  its  source  in  molecular  motions  of  the  atoms  of 
substances  in  nature.     But  this  definition,  although  of  great 
value  in  aiding  the  popular  comprehension,  requires  explana- 
tion, inasmuch  as  motion,  or  a  particular  kind  of  motion,  as 
an  abstract  idea,  does  not  involve  the  idea  of  force  or  energy. 

5.  It  is  not  difficult  to  conceive  of  the  existence  of  power,  6r 


2  HEAT. 

energy  in  connection  with  motion,  however,  if  the  motion  be 
that  of  a  mass  or  heavy  body. 

6.  Actual  energy,  living  force,  vis  viva,  etc.,  are  expressions 
employed  by  different  writers  to  designate  the  capacity  for  per- 
forming work  which  is  inherent  in  ther  motion  of  bodies,  and 
which  results  from  the  velocity  and  mass  combined ;  the  mea- 
sure of  this  capacity,  or  actual  energy,  being  the  mass  multiplied 
by  half  the  square  of  the  velocity. 

7.  There  is  no  principle  of  mechanics  more  universally  re- 
cognized than  this,  and  no  law  more  commonly  employed.     In 
the  ordinary  movements  of  most  animals  its  applications  are  so 
frequent  and  essential  that  it  may  be  said  to  be  a  source  of 
economy  in  muscular  effort,  while  it  performs  a  principal  part 
in  nearly  all  devices  for  the  utilization  of  the  various  forces  of 
nature. 

8.  The  condition  of  a  body,  the  particles  of  which  are  agi- 
tated by  this  peculiar  heat-motion,  is  thus  a  condition  of  energy. 
The  body  has  a  certain  amount  of  actual  energy  due  to  its  mass 
and  the  resultant  motion  of  its  particles  or  molecules. 

9.  This  energy  may  be  expended,  just  as  the  energy  of  the 
fly-wheel  may  be  expended,  in  overcoming  resistances  and  per- 
forming wor7c ;  or  it  may  be  increased  by  having  the  velocity 
of  heat-motion  increased,  just  as  the  energy  of  the  fly-wheel  is 
increased  by  energy  stored  up  in  an  increased  velocity. 

10.  Tn  the  case  of  the  fly-wheel,  an  increase  in  velocity  can  be 
produced  by  the  application  of  some  external  force,  and  a  dimi- 
nution of  velocity,  by  the  overcoming  of  some  resistance,  such  as 
the  raising  of  a  weight,  the  compression  of  a  fluid  or  spring,  or 
the  disintegration  of  some  material. 

11.  In  the  first  case  the  application  of  an  external  force 
develops  motion  in  the  mass  of  the  fly-wheel,  and  the  work  of 
this  force  is  thus  transformed,  or  converted,  into  the  living  force 
or  energy  of  the  fly-wheel.     In  the  second,  living  force  disap- 
pears, with  the  diminution  of  motion,  and  is  transformed  or  con- 
verted into  external  work. 

12.  The  living  force  which  constitutes  the  energy  or  power  of 
heat,  although  not  accompanied  by  the  visible  finite  motion  of 
the  whole  mass  of  a  body  in  one  direction,  is  nevertheless  of  the 
same  nature  and  acts  by  the  same  law. 

13.  The  exact  nature  of  the  heat-motion  of  the  particles  of 
substances  has  not  been  determined,  and  the  ultimate  at  range- 


HEAT.  3 

ment  of  these  particles  in  the  formation  of  bodies  is  still  a  mat- 
ter of  speculation. 

14.  There  is,  however,  a  universal  acquiescence,  on  the  part  of 
scientific  men,  in  the  theory  that  the  atoms  or  molecules  of  all 
substances  have  a  vibratory  or  oscillating  motion  of  a  peculiar 
character,  which  may  be  called  heat-motion. 

15.  The  distance  passed  over  by  each  atom  at  each  vibration 
is  inconceivably  small,  so  small  as  to  elude  the  senses,  but  the 
number  of  vibrations  in  an  ordinary  unit  of  time  is,  on  the  other 
hand,  inconceivably  great. 

All  substances  possess  this  heat-motion.  The  absence  of  it 
in  nature  cannot  be  conceived  without  carrying  with  this  con- 
ception the  idea  of  the  destruction  of  animal  life,  and  a  com- 
plete change  in  the  elements  as  they  are  now  presented  to  us. 

So  that  under  this  view,  all  solids,  liquids,  and  gases,  as  far  as 
now  known,  being  animated  by  this  peculiar  motion,  heat  may 
be  regarded  as  a  property  of  matter. 

According  to  the  dynamic  theory,  a  change  in  the  heat  of  a 
body  implies  simply  a  change  in  the  velocity  of  vibration  of  the 
particles,  and  the  particles  having  weight  or  mass,  a  change  of 
heat  involves  the  development  or  disappearance  of  living  force. 

16.  The  various  phenomena  connected  with  heat  may  be  di- 
vided into  three  classes : 

1.  The  action  of  the  heat  of  a  body  as  a  source  of  power  or 
energy  in  performing  work  external  to  the  ~body  in  which  it 
exists,  and  internally  in  changing  the  relative  positions  of  the 
particles ',  or  producing  expansions  and  contractions  of  volume  ; 
and,  conversely,  the  generation  of  heat  in  a  ~body  accompanied 
~by  change  of  volume  and  density  by  the  application  of  external 
work. 

2.  The  changes  which  bodies  undergo  in  form  and  other 
properties  when  subjected  to  changes  of  heat. 

3.  The  transfer  of  heat  from  one  body  to  another. 

17.  A  consideration  of  the  third  class  of  phenomena,  the 
transfer  of  heat,  involves  the  introduction  of  an  element  in  the 
material  world,  the  existence  of  which  cannot  be  made  evident 
to  the  senses  in  any  ordinary  manner,  but  which  is  proved  by 
analogy  and  scientific  reasoning. 

18.  While  the  molecules  or  atoms  of  substances  are  aggre- 
gated in  the  closest  proximity  and  have  incessant  motion,  there 
is  presumed  to  be  a  gaseous  or  ethereal  substance  pervading  all 


4  HEAT. 

space,  the  particles  of  which  are  so  small,  compared  with  ordi- 
nary material  atoms,  that  the  ether  permeates  the  spaces  between 
the  atoms  of  substances,  and  is  capable  of  being  set  in  motion 
or  vibration  by  the  motions  of  these  atoms. 

19.  On  the  other  hand,  motion  communicated  to  this  ethereal 
medium  at  a  point  external  to  a  body,  and  transmitted  in  the 
form  of  waves,  may,  through  the  action  or  impact  of  these  waves 
with  the  particles  of  a  body,  impart  motion  to  them. 

20.  Popular  attention  is  often  directed  to  these  wave-motions 
as  the  source  and  cause  of  heat  and  light.     But  the  view  most 
generally  accepted  appears  to  be  that  which  places  the  source 
of  energy  in  the  incessant  motion  of  the  molecules  of  substances, 
and  regards  the  ethereal  substance  as  a  medium  of  transfer, 
just  as  the  atmosphere  is,  in  an  analogous  manner,  the  medium 
of  transfer  of  the  vibrations  of  bodies  in  the  production  of  sound. 

21.  The  radiation  of  heat  is  then  but  a  wave-motion  com- 
municated to  the  ethereal  medium  by  the  action  of  the  atoms  or 
molecules  of  bodies.     A  heated  body  loses  heat-motion,  and  liv- 
ing force,  in  sending  off  waves  in  this  medium ;  and  another 
body,  in  the  path  of  these  waves,  will  have  the  motions  of  its 
molecules  increased  in  velocity  and  will  become  heated.     The 
particles  of  the  ethereal  medium,  having  weight  or  mass,  possess 
energy  when  in  motion  and  impart  this  energy  to  the  material 
atoms. 

Thus  arise  the  phenomena  of  radiwnt  heat  and  light ;  pheno- 
mena which,  when  studied  and  observed  in  reference  to  the 
wave-motions  alone,  present  all  those  interesting  effects  of  heat 
and  light  which  arise  from  different  lengths  and  velocities  of 
the  waves — interference,  polarization,  diffraction  and  reflection- 
giving  rise  to  different  colors,  as  well  as  different  heating  effects, 
from  the  same  source  of  motion. 

22.  These  phenomena  belong  to  the  general  subject  of  phy- 
sics, and  may  be  omitted  in  the  discussion  of  heat  as  a  source  of 
energy.     It  is  to  be  remarked,  however,  that  one  of  the  unset- 
tled questions  in  the  views  of  scientific  men  on  this  subject,  is, 
whether  the  origin  of  heat-motion  in  matter  lies  in  the  motion 
of  the  particles  of  the  ethereal  medium,  or  solely  in  the  motion 
of  the  atoms  of  bodies,  or  in  both  combined. 

23.  The  view  generally  accepted  is  that  stated   above,  the 
origin  of  force  being  supposed  to  exist  in  the  motions  of  the 
atoms,  or  molecules. 


HEAT.  5 

24.  Under  this  view  the  first  and  second  classes  of  phenomena 
become  intelligible,  and  may  be  subjected  to  rigorous  analysis 
as  well   as   rational  explanation.      Every  body — by  which  is 
to  be  understood  a  definite  quantity  by  weight  or  volume  of  a 
given  substance — is  supposed  to  be  composed  of  heavy  atoms, 
each  of  which  is  in  incessant  motion,  though  the  velocities  of 
oscillation  of  all  the  particles  may  not  be  identical.     There  re- 
sults, however,  a  certain  mean  or  average  velocity  of  motion, 
and  the  living  force  of  the  whole  body  due  to  the  heat-motion, 
of  all  the  particles  may  be  expressed  by  the  well-known  law  of 
the  mass  multiplied  by  one-half  the  square  of  the  mean  velocity. 

25.  By  algebraic  symbols,  if  v  represent  the  mean  velocity 
of  the  heat-motion  in  a  body  the  mass  of  which  is  M,  the  actual 
energy  due  to  this  heat-motion  will  be 


and  if  vx  represent  any  other  velocity,  the  actual  energy  corre- 
sponding to  this  velocity  will  be 


and  the  difference  M( — - — -  j  will  represent  the  expenditure 

of  energy,  or  the  work  of  inertia,  due  to  the  change. 

If  there  is  a  loss  of  heat,  or  a  loss  of  .velocity,  energy  will  be 
expended,  and  if  a  gain  of  heat,  energy  will  be  stored. 

26.  Heat  as  a  source  of  energy  may  therefore  be  regarded 
simply  as  the  work,  of  the  force  of  inertia.  *  As  the  fly-wheel 
possesses  power  derived  from  its  mass  and  rapid  motion  to  drive 
machinery,  so  all  substances  possess  energy,  derived  from  the 
rapid  oscillation  of  the  individual  molecules,  to  perform  work, 
when  these  oscillations  are  diminished.     The  rapid  oscillations 
of  the  particles  of  steam,  or  gas,  constitute  the  source  of  power 
in  heat-engines.     These  particles,  enclosed  by  a  cylinder  one 
end  of  which  is  movable,  strike  the  movable  end,  or  piston,  and 
give  it  motion  ;  the  effect  on  the  heat-motion  of  the  particles  of 
steam,  or  gas,  being  to  diminish  the  living  force  of  the  whole 
mass  of  steam  enclosed  by  a  quantity  which  is  identical  with 
the  work  performed  by  the  piston. 

27.  It  is,  then,  the  force  of  inertia  which  drives  mills,  steam- 
ships, and    factories,   under    the    name    of    heat,   and  which 


6  HEAT. 

lias  become,  in  a  new  and  unexpected  manner,  a  universal  aid  to 
man. 

28.  The  STEAM-BOILER  is  the  apparatus  by  which,  through 
the  process  of  combustion,  a  rapid  degree  of  heat-motion  is 
developed  in  the  fuel  and  gaseous  products  of  combustion,  and 
transferred  to  the  particles  of  water ;  the  steam-engine  is  the 
apparatus  in  which  the  heat-motion  is  again  partially  destroyed, 
the  inertia  developed  by  this  change  being  the  force  which  per- 
forms the  work  of  the  machine. 

29.  When  work  is  thus  performed,  there  is  necessarily  an 
exact  equivalence  between  the  cause  and  effect.     In  ordinary 
mechanics  it  is  well  known  that  the  expression 


rationally  interpreted,  denotes  that  the  work  performed  by  the 
inertia  of  the  mass  M,  when  its  velocity  is  changed  from  v  to 
v,  is  equivalent  to  the  work  estimated  by  multiplying  a  force 
p  by  a  distance  h  ;  to  find  the  value  of  the  product  p  xli,  it  is 
only  necessary  to  give  numerical  values  to  the  quantities  M,  v,  and 

AA/- 

vr    M  is  equal  to  — ,  the  weight  divided  by  the  numerical  ex- 

to 

pression  for  the  force  of  gravity ;  v  and  va  are  usually  determin- 
ed by  observation,  and  are  expressed  in  feet  per  second. 

30.  When  this  expression  represents  the  work  performed  by 
the  inertia  for  a  given  change  of  heat-motion,  a  difficulty  presents 
itself  in  an  attempt  to  give  numerical  values  to  the  quantities. 

The  mass  may  be  found  as  before,  being  the  weight  of  the 
body  divided  by  the  force  of  gravity,  numerically  expressed;  but 
the  velocities  v  and  vl  belong  to  motions  which  elude  the  senses. 

The  second  member  of  the  equation,  P  x  h,  may,  however,  be 
expressed  in  the  same  numerical  terms  as  before,  a  pressure  or 
weight  multiplied  by  the  distance  or  space  through  which  it  acts. 
It  is  obvious  that  where  the  whole  effect  of  a  change  of  heat  is  the 
performance  of  a  certain  work,  p  x  h,  if  the  external  work  can 
be  measured  the  numerical  value  of  the  first  member  may  be 
determined. 

31.  Experiments  of  this  character  have  been  performed,  and 
those  of  Mr.  Joule,  from  having  been  the  first  thorough  and 
systematic  experiments  made  with  this  object,  have  caused  his 
name  to  be  ^i.nected  most  prominently  with  such  researches. 


HEAT.  7 

His  experiments  were  made  with  an  apparatus  consisting  of 
a  small  cylindrical  case  filled  with  water,  in  which  blades  were 
made  to  revolve,  by  the  application  of  power  furnished  by  a 
weight  attached  to  a  cord  which  passed  over  a  fixed  pulley. 
The  water  in  the  case  was  prevented  from  rotating  in  a  vortex 
with  the  blades,  so  that  the  only  effect  of  the  motion  of  the 
blades  was  to  produce  friction  among  the  particles  of  water. 
This  friction  developed  heat  in  the  water  ;  and  the  work  ex- 
erted to  drive  the  blades,  viz.,  a  weight  falling  through  a  height, 
was  measured. 

32.  A  numerical  expression  for  the  work  was  thus  easily  found. 
In  mechanics,  it  is  well  known  that  a  unit  of  work  is  composed 

of  two  other  units,  a  unit  of  weight  and  a  unit  of  distance  —  in 
English  measures  one  pound,  and  one  foot  ;  so  that  one  pound 
raised  one  foot  high  is  called  a  unit  of  work,  or  a  foot-pound. 

33.  The  question  then  occurs,  how  shall  the  change  of  heat 
which  a  given  amount  of  work  produces,  be  measured  ?    There 
must  necessarily  be  some  unit  for  such  measurement  ;  and  since 
the  velocities  of  the  particles  cannot  be  observed,  recourse  is 
had  to  an  arbitrary  unit  of  heat. 

34.  It  might  be  presumed  that  if  a  body  be  exposed  continu- 
ously to  the  same  cooling  influences  for  a  certain  length  of 
time,  the  effects  would  be  equal  in  equal  times  ;  or  if  a  body  be 
exposed  continuously  to  the  same  influence  which  increases  the 
velocity  of  heat-motion,  or  the  same  heating  influences,  the  effects 
of  these  influences  would  be  equal  in  equal  times  ;  popularly 
speaking,  the  quantity  of  heat  which  would  leave  or  enter  the 
body  in  equal  times  would  be  equal.     So  that  if  we  always  had 
the  same  source  of  heating  or  cooling,  this  quantity  of  heat 
might  be  measured  by  the  time,  and  a  heat-unit  based  on  time 
might  be  employed. 

35.  If  we  were  to  represent  by  1  the  quantity  of  heat  lost  or 
gained  in  one  unit  of  time,  we  could  represent  by  1  multiplied 
by  a  number  of  seconds  any  other  quantity  of  heat,  and  the  ex- 
pression 


would  be  represented  in  terms  of  this  unit,  and  it  would  only 
remain  to  determine  experimentally  how  many  units  of  work 
correspond  to  one  unit  of  heat,  or  the  value  of  P  x  h  for  one  unit 
of  heat. 


8  HEAT. 

36.  But  we  have  not  always  the  same  constant  source  of  heat- 
ing or  cooling.     On  the  contrary,  heat-motion  is  developed  or 
destroyed  by  a  great  variety  of  physical  agencies,  such  as  chemi- 
cal composition,  decomposition,  electricity,  radiation,  and  con- 
duction.    Some  other  arbitrary  unit  must  therefore  be  found, 
and  advantage  is  taken  of  the  property  which  all  substances 
possess,  of  changing  form  when  heated  or  cooled,  independently 
of  the  source  of  heating  or  cooling. 

37.  It  is  known,  from  observation  and  experience,  that  sub- 
stances generally  expand  when  heated  and  contract  in  volume 
when  cooled,  and  it  is  further  known  that  these  phenomena  are 
independent  of  the   nature   of   the   source  which  causes  the 
changes,  so  that  generally,  in  solids,  liquids,  and  gases,  a  given 
change  of  heat  is  accompanied  by  a  corresponding  change  in 
the  volume  of  the  body  heated  or  cooled,  whatever  may  have 
been  the  source  of  heating  or  cooling. 

38.  This  law  is  so  invariable  that  the  amount  of  expansion  of 
a  body  may  be  taken  to  indicate  changes  of  heat. 

39.  The  construction  of  the  common  thermometer  is  based  on 
this  idea.     The  thermometer,  when  applied  to  a  body,  indicates 
the  degree  or  velocity  of  heat-motion   of  the   molecules,  the 
heat-motion  being  more  or  less  rapid  according  to  the  expan- 
sion of  the  fluid  of  the  thermometer  as  indicated  by  its  scale. 

40.  We  thus  have  what  are  known  as  degrees  of  heat  or  de- 
grees of  temperature,  the  term  temperature  indicating  a  con- 
dition of  the  body  merely,  and  changing  in  a  manner  propor- 
tional to  the  change  of  heat — the  term  temperature  in  this  re- 
spect being  somewhat  analogous  to  the  term  velocity,  in  treating  of 
ordinary  motions  of  heavy  bodies.  And  because  the  thermometer 
is  brought  into  a  condition  of  heat  in  equilibrium  with  that  of 
the  body  to  which  it  is  applied,  by  mere  proximity,  or  contact,  it 
may  be  said  to  indicate  the  sensible  heat  of  the  body,  or  power 
of  the  body  to  communicate  heat  to  other  bodies. 

41.  If  now  we  take  a  pound  of  water,  and  cause  a  change  of 
heat  indicated  by  a  change  of  temperature  of  one  degree  of  the 
thermometer,  we  have  all  the  elements  necessary  for  a  heat-unit. 

The  mass  or  weight  is  known,  and  we  have  found  a  measur- 
able quantity — the  volume  of  the  mercury  or  other  substance 
employed  as  a  thermometer — which  changes  with  the  changes  of 

M  va 
heat,  or  as  — —  changes. 


HEAT.  9 

42.  We  may  now  assume  the  change  of  heat  corresponding  to 
one  pound  of  water  raised  in  temperature  one  degree  to  be  one 

UNIT  OF  HEAT. 

For  water,  the  quantity  of  heat,  measured  by  heat-units,  cor- 
responding to  any  change  of  heat,  may  then  be  represented  by 
the  number  of  pounds  of  water  multiplied  by  the  number  of 
degrees  of  the  thermometer  which  indicates  the  change  of  tem- 
perature. 

43.  It  was  found  by  Joule,  in  the  experiments  referred  to, 
that  one  unit  of  heat  corresponds,  or  is  equivalent  to,  772  foot- 
pounds of  work,  water  being  taken  at  a  temperature  of  39.1° 
Fahrenheit,  its  point  of  maximum  density.     This  experimental 
determination  has  been  abundantly  verified  by  other  experi- 
ments made  by  different  philosophers,  in  various  modes,  so  that 
772  foot-pounds  is  now  known  as  the  dynamic  equivalent  of  a 
unit  of  heat  in  English  measures.     In  French  measures  the  unit 
of  heat  is  called  the  Calorie,  and  is  the  quantity  of  heat  which 
corresponds  to  a  change  of  heat  indicated  by  one  degree  of  the 
centigrade  thermometer,  in  one  kilogram  (2.20  Ibs.)  of  water, 
the  water  being  taken  at  its  maximum  density.     This  unit  is 
equivalent  in  French  measures  to  423.55   kilogram  metres,  or 
423.55  kilograms  raised  one  metre. 

44.  The  fundamental  law  of    Thermodynamics,  or  of  the 
dynamic  theory  of  heat,  is  involved  in  what  has  already  been 
stated. 

Seat  and  mechanical  energy  are  mutually  convertible ?,  the  con- 
version being  the  transformation  of  living  force  into  work,  or  the 
reverse;  one  unit  of  heat  being  equivalent  to  772  foot-pounds. 

The  rational  interpretation  of  the  term  unit  of  heat  employed 
in  this  enunciation,  is  that  the  work  of  inertia  of  the  particles 
of  water,  or  the  change  of  living  force,  which-  occurs  when  the 
heat  of  one  pound  of  water  is  changed  by  a  quantity  represent- 
ed by  1°  Fahrenheit,  is  equivalent  to  772  foot-pounds. 

45.  In  the  application  of  mathematics  to  the  subject  of  heat 
this  is  called  a  quantity  of  heat  represented  by  unity.     A  quan- 
tity of  heat  represented  by  any  number  would  be  this  quantity 
repeated  as  many  times  as  there  are  units  in  the  number. 

W 

If   W  represent  any  quantity  of  work  in  foot-pounds,  -=^ 

will  represent  the  equivalent  quantity  of  heat  expressed  in  heat- 
units,  one  expression  representing  the  effect  and  the  other  the 


10  HEAT. 

cause ;  or,  Q,  expressed  in  heat-units,  multiplied  by  772,  will  give 
the  number  of  foot-pounds  equivalent  to  a  given  quantity  of 
heat. 

46.  Passing  to  other  substances,  it  may  be  stated  that  the  heat- 
unit  of  any  substance  is  that  quantity  of  heat  which  corresponds 
to  a  change  of  1°  in  the  temperature  of  1  pound  of  the  sub- 
stance. 

47.  The  heat-units,  or  specific  heats  of  different  bodies,  are  all 
different,  as  the  name  implies ;  and  as  it  is  convenient  to  have 
but  one  unit  of  heat,  that  of  water  is  chosen  as  this  unit,  and 
the  specific  heats  of  other  substances  are  expressed  relatively  to 
that  of  water. 

48.  Tables  giving  the  specific  heats  of  substances,  so  express- 
ed, may  be  found  in  nearly  all  standard  works  which  treat  of 
heat.     A  very  complete  set  of  such  tables  is  given  in  Watts's 
Chemistry.     It  is  to  be  observed,  in  regard  to  specific  heats,  that 
all  known  substances,  except  hydrogen,  require  less  heat  for  a 
change  of  temperature  of  one  pound  of  the  substance  one  de- 
gree than  that  which  is  required  for  water. 

49.  This  in  an  accidental  property  of  water,  but  the  result  is, 
that  in  a  table  of  specific  heats  the  numbers  which  represent  the 
specific  heats  are,  with  the  exception  of  that  for  hydrogen,  less 
than  unity. 

50.  To  find  the  quantity  of  heat  corresponding  to  any  given 
change  of  temperature,  in  a  given  quantity  of  any  substance,  re- 
quires, then,  three  factors — the  number  of  pounds ,  the  change 
of  temperature  in  degrees ,  and  the  specific  heat. 

This  last  factor  for  water  (at  39.1°,  or  maximum  density) 
being  unity,  and  for  other  substances,  'the  specific  heats  may  be 
found  from  the  tables.  A  quantity  of  heat  represented  by  Q, 
that  is,  a  change  of  heat  equivalent  to  Q  expressed  in  heat-units, 
may  be  expressed  by  symbols  thus : 

Q  —  w  x  c  x  F 

w  being  the  weight  of  the  body,  c  the  .specific  heat,  F  the 
number  of  degrees  of  change  of  temperature. 

51.  It  is  evident  that  if  three  of  the  above  quantities  are 
the  known  quantities  in  any  problem,  the  fourth  can  be  deter- 
mined. 

52.  The  following  tables,  taken  from  Watts's  Chemistry,  ex- 
hibit the  mean  specific  heats  of  the  substances  named : 


HEAT.  11 

TABLE  I. 
SOLIDS.  Specific  Heat. 

Copper 0.0951 

Gold 0.0324 

Iron 0.1138 

Lead 0.0314 

Platinum 0.0324 

Silver 0.0570 

Tin 0.0562 

Zinc 0.0955 

Brass 0.0939 

Glass 0.197T 

Ice 0.5040 

Sulphur 0.2020 

Charcoal 0.2410 

Alumina 0.1970 

Stones,  Bricks,  etc.,  about 0.2200 

LIQUIDS. 

Water 1.0000 

Lead       (melted) 0.0402 

Sulphur        «         0.2340 

Bismuth        "       0.0363 

Tin                "       0.0637 

Mercury 0.0332 

Alcohol 0.6150 

Fusel  Oil 0.5640 

Benzine 0.4500 

Ether , 0.5034 

GASES. 

At  constant  pressure.    At  constant  volume. 

Air 0.238  0.169 

Oxygen 0.218  0.156 

Hydrogen 3.405  2.410 

Steam-Gas 0.480  0.346 

Carbonic  Acid 0.217  

Nitrogen 0.244  

Olefiant  Gas 0.404  0.173 

Carbonic  Oxide 0.245  0.237 

Ammonia..                               0.508  0.299 


12  HEAT. 

53.  The  above  specific  heats  are  average  values,  taken   at 
temperatures  which  usually  come  under  observation  in  techni- 
cal applications.     The  actual  specific  heats  of  all  substances  in 
the  solid  or  liquid  states  increase  slowly  as  the  body  expands,  or 
as  the  temperature  rises,  and  when  great  accuracy  is  required 
tables  of  specific  heats  may  be  consulted  which  will  give  these 
quantities  with  greater  definiteness  at  special  temperatures. 

54.  The  following  examples  will  illustrate  the  use  of  the 
tables  in  solving  problems  relating  to  changes  of  heat  and 
changes  of  temperature. 

Example  1. 

Let  it  be  required  to  ascertain  what  rise  of  temperature  Fahr. 
will  result  from  the  transfer  of  1,000  units  of  heat  by  any  pro- 
cess whatever,  such  as  radiation  or  friction,  to  100  Ibs.  of  iron 
taken  at  any  ordinary  temperature. 

In  the  expression 

Q  —  w  x  c  x  F 

Q  =  1,000  units  of  heat, 

c  =  0.1138  specific  heat  of  iron  from  tables, 

w  =  100  =  weight  of  iron  as  enunciated, 

F  the  unknown  quantity  to  be  determined,  we  have 


_-  . 

w  x  c        11.38 

55.  The  specific  heats  of  gases  are  given  for  constant  pressure 
and  for  constant  volume.  It  is  well  known  that  a  gaseous  sub- 
stance, to  be  treated  as  a  quantity  or  body  having  volume,  must 
be  confined  by  some  envelope  or  within  an  enclosure  through 
the  sides  of  which  the  gas  cannot  escape.  Such  an  enclosure 
may  have  an  invariable  volume,  that  is,  its  sides  may  not  yield 
to  any  pressure  from  the  interior,  or  it  may  have  a  variable 
volume,  as  when  air  is  enclosed  in  an  elastic  envelope  or  within 
a  cylinder  having  one  end  movable.  The  effect  of  transferring 
an  additional  quantity  of  heat  to  a  given  weight  of  gas,  is  to 
cause  it  to  expand  in  volume  if  the  envelope  will  admit  of  ex- 
pansion. 

If  the  envelope  expands  sufficiently  to  adjust  the  new  volume 
to  the  external  pressure,  this  external  pressure  being  constant, 
the  specific  heats  to  be  employed  in  determining  quantities  of 
heat  are  those  given  under  the  head  constant  pressure. 


HEAT.  13 

If  the  volume  remain  invariable,  the  specific  heats  to  be 
used  are  those  under  the  head  constant  volume. 

Example  2. 

56.  Let  1  Ib.  of  air  be  enclosed  in  a  vessel  of  invariable  vol- 
ume, and  let  it  be  required  to  find  the  number  of  units  of  heat 
to  be  transferred  to  or  from  this  quantity  of  air  to  cause  a 
change  of  temperature  of  50°  Fahr. :  we  will  have 

Q  =  w  x  c  x  F 
where  w  —  1  Ib. 

c  =  specific  heat  of  air  at  constant  volume. 
F  =  50°. 

Q  =  1  x  0.169  x  50°  =  8.45  units  of  heat. 
If  this  air  be  allowed  to  expand  while  being  heated  under  a 
constant  pressure,  the  quantity  of  heat  required  would  be 

Q,  =  1  x  50  x  .238  =  11.9  units  of  heat, 
and  the  equivalent  in  work  would  be 

Qi  x  772  =  11.9  x  772  =  9186.8  foot-pounds.    Hr 
In  this  case  the  air  is  not  only  heated  to  the  same  degree  as 
before,  but  it  expands  by  a  certain  quantity,  and  the  work  of 
expansion   against   a  constant  pressure  requires  an  additional 
quantity  of  heat. 

57.  Action  of  Heat  upon  Bodies  in  Nature. — The  general 
theory  of  heat  having  been  considered,  we  are  led  in  the  next 
place  to  examine  the  effect  which  a  change  in  heat-condition 
produces  in  bodies  in  nature. 

With  this  end  in  view  it  is  desirable,  first,  to  classify  bodies 
according  to  the  forms  and  properties  which  they  assume  or  ex- 
hibit as  they  are  ordinarily  presented  to  our  senses,  viz. :  Solids, 
Liquids,  Gases. 

58.  Solids. — A  solid  body  is  a  body  the  molecules  of  which, 
though  in  a  state  of  incessant  vibration,  nevertheless  are  retained 
in  such  a  state  of  equilibrium  between  the  attraction  of  the 
molecules  for  each  other  and  the  oscillations  due  to  heat,  that 
the  body,  as  a  whole,  retains  the  state  which  is  called  solid. 
The  conditions  of  equilibrium  of  the  molecules,  when  there  is 
no  change  in  the  heat  of  the  body,  can  only  be  altered  by  ex- 
ternal forces. 

59.  Liquids. — In  the  liquid  state  the  molecules  of  the  body 


14  HEAT. 

I 

move  freely  among  themselves,  but  are  not  permanently  attached 

to  each  other.  In  other  words,  a  single  molecule  may  transfer  its 
contact  from  one  set  of  molecules  to  another  set,  subject  to  the 
condition  that  the  particles  or  aggregated  molecules  remain  in 
mutual  contact  like  so  many  minute  spheres  or  globules,  rolling 
freely  upon  each  other,  but  still  retained  in  mass  by  the  attract- 
ive forces  which  act  through  their  point  of  contact. 

60.  Gases. — In  the  gaseous  state  the  molecules  are  removed 
entirely  beyond  the  spheres  of  their  mutual  attractions.     When 
the  molecules  of  a  gas  meet  they  repel  each  other,  and  thus  a  gas 
will  expand  indefinitely  if  it  be  not  enclosed  within  an  envelope. 

Nearly  all  substances  in  nature,  as  far  as  known  at  present, 
are  capable  of  assuming  all  of  the  above  states  under  certain 
conditions  of  heat ;  the  action  of  heat  upon  a  solid  being  first 
to  cause  expansion  or  increase  of  volume,  then  fusion  or  melt- 
ing, a  change  from  the  solid  to  the  liquid  state,  and  as  the  heat 
of  the  body  increases,  a  further  change  from  the  liquid  to  the 
gaseous  condition. 

Some  gases,  however,  known  as  permanent  gases,  viz.,  air, 
oxygen,  nitrogen,  nitric  oxide,  carbonic  oxide,  and  marsh-gas, 
have  never  been  obtained  in  the  liquid  state. 

61.  A  definite  quantity  of  any  given  substance  requires  three 
conditions  for  its  existence  in  a  separate  and  distinct  form ; 
these  are  volume,  pressure,  and  temperature. 

By  volume  is  to  be  understood  the  actual  space  occupied  by 
the  substance  without  regard  to  the  form  of  that  space;  by 
pressure,  the  resistance  of  the  external  envelope  of  the  body  to 
its  expansion ;  and  by  temperature,  the  condition  of  heat-motion 
of  its  particles. 

The  effect  of  a  change  of  heat  must  therefore  be  the  same 
for  all. 

62.  The  transfer  of  heat  to  a  solid  not  only  causes  an  increase 
of  molecular  vibration,  which  is  exhibited  by  an  increase  of  tem- 
perature, but  an  expansion,  which  consists  in  the  separation  of 
the  particles  from  each  other,  or  an  increase  of  volume;  but  this 
expansion  involves  the  overcoming  of  the  external  pressure  of 
the  air  or  other  enveloping  medium. 

63.  In  the  case  of  liquids,  a  transfer  of  heat  to  the  liquid  pro- 
duces precisely  the  same  effects  as  in  the  case  of  a  solid ;  in- 
crease of  molecular  vibration,  disintegration,  involving  expan- 
sion of  volume,  and  overcoming  of  the  external  pressure. 


HEAT.  15 

64.  In  the  case  of  perfect  gases,  the  molecules  having  already 
become  entirely  separated,  the  effect  of  a  transfer  of  heat  to  a 
gas  is  exhibited  simply  in  increase  of  vibration  of  the  particles, 
or  increase  of  sensible  heat  (temperature),  and  the  overcoming 
of  the  external  pressure. 

65.  When  heat  is  abstracted  from  a  body,  the  effects  described 
above  are  all  reversed.     The  molecular  oscillation  is  diminished, 
the  volume  contracts,  and  the  external  pressure,  acting  through 
the  volume  passed  over  by  the  contracting  envelope,  will  per- 
form work  which  appears  in  the  heat  abstracted. 

66.  These  general  laws  may  be  illustrated  or  explained  in  a 
very  simple  manner,  according  to  the  fundamental  theory  of  heat 
which  has  been  enunciated,  by  the  use  of  algebraic  symbols. 

Suppose  a  definite  quantity  of  any  body,  solid,  liquid,  or 
gaseous,  to  receive  heat  from  some  external  source.  Let  the 
quantity  of  heat  received,  expressed  in  units  of  heat,  be  denoted 
by  Q.  The  body  will  undergo  the  following  changes  : 

1st.  An  increase  of  molecular  movement  involving  an  in- 
crease of  actual  energy  or  living  force,  which  may  be  represented 
by  A. 

2d.  A  certain  amount  of  expansion  or  change  of  position  of 
the  particles,  which  involves  a  certain  amount  of  work  in  over- 
coming the  attractive  forces  of  the  body,  which  may  be  repre1 
sented  by  B. 

3d.  The  change  of  volume  involves  the  work  of  overcoming 
the  external  pressure  to  an  amount  which  may  be  represented 
by  c  ;  and  since  Q  is  expressed  in  units  of  heat,  and  A,  B,  and 
c  are  supposed  to  be  expressed  in  units  of  work  —  foot-pounds 
—  we  shall  have,  for  the  total  effect  of  the  heat  transferred, 

A    +    B    +    C 


In  solids  and  liquids,  the  expansion  being  small  in  compari- 
son with  the  original  volume,  c  will  be  very  small,  and  may  be 
left  out  of"  consideration,  and  the  expression  will  become. 

A    +     B 

Qr  -773- 

In  perfect  gases,  the  forces  of  attraction  of  the  molecules  hav- 

Jr  o  * 

ing  been  entirely  overcome,  the  quantity  B  will  disappear,  and 
we  shall  have 

A    +    O 


16  HEAT. 

This  is  the  most  important  case  in  technical  applications,  be- 
cause the  employment  of  heat  as  a  source  of  power  is  usually 
through  the  medium  of  gases,  and  this  expression  shows  that 
the  only  effects  of  a  change  of  heat  are  a  change  in  the  mole- 
cular vibrations  of  the  gas,  involving  living  force,  and  the  over- 
coming of  external  pressures. 

If  heat  be  abstracted,  the  effects  are  similar  but  reversed ;  the 
external  pressure  acts  in  the  same  direction,  and  the  oscillations 
of  the  particles  or  molecules  are  diminished. 

67.  .In  the  case  of  bodies  which  are  known  by  observation  to 
contract  when  heated,  at  certain  temperatures,  or  to  expand  when 
cooled,  as  water  and  some,  alloys,  the  sign  of  the  term  c  will  be 
reversed  at  these  points,  and  the  expression  will  furnish  an  ex- 
planation of  the  peculiar  phenomenon,  that  under  these  circum- 
stances an  increase  of  external  pressure  will  lower  the  tempera- 
ture of  fusion  or  congelation — a  fact  announced  by  Prof.  James 
Thomson,  and  afterwards  verified  by  experiment  by  Prof.  Wm. 
Thomson. 

68.  The  above  laws  are  general ;  and  bodies  which  expand 
when  heated  under  constant  pressure,  usually  regain  their  origi- 
nal volume  when  cooled  to  their  original  temperature. 

There  are,  however,  some  remarkable  exceptions.  It  is  well 
known  that  water  has  'a  point  of  maximum  density,  or  a  point 
at  which  the  volume  of  a  given  quantity  is  the  least.  This 
temperature  is  39.1°  Fahr.  If  water  be  cooled  below  that  tem- 
perature, it  expands,  and  if  heated  from  a  point  below  that  tem- 
perature, it  contracts  until  that  temperature  is  reached. 

Another  exception  is  Hose's  fusible  metal.  There  is  a  certain 
temperature  of  maximum  expansion  beyond  which,  if  it  be 
heated,  it  contracts.  Another  remarkable  exception  is  given  by 
Balfour  Stewart,  as  results  of  experiments  by  Fizeau,  which 
show  that  iodide  of  silver  contracts  by  heat  and  expands  by 
cold  at  any  point  between  the  temperatures  10°  and  70°  Centi- 
grade. u 

Moreover,  the  enunciation  of  the  law  that  bodies  when  heated 
and  then  cooled  to  the  original  temperature,  regain  their  origi- 
nal volume,  requires  a  further  condition  in  the  case  of  most 
solids.  The  cooling  must  be  slow  and  gradual.  If  abrupt  and 
sudden,  the  original  volume  may  not  be  regained,  and  peculiar 
effects  are  often  produced  which  are  difficult  of  explanation, 
such  as  brittleness  and  hardness. 


HEAT.  17 

The  process  of  annealing,  or  slow  cooling,  is  essential  when 
certain  conditions  in  these  respects  are  desired. 

Assuming  as  the  general  law  that  bodies  expand  when  heated, 
and  that  nearly  all  bodies  may  be  made  to  assume  the  three 
conditions  described  as  solid,  liquid,  and  gaseous,  we  may  ex- 
amine the  phenomena  which  occur  when  any  substance  passes 
under  the  influence  of  heat,  from  the  solid  to  the  liquid  and 
gaseous  conditions. 

69.  Coefficient  of  Expansion. — The  rate  of  expansion  of  a 
body  is  the  increase  of  volume  which  takes  place  for  equal  in- 
crements of  temperature,  the  volumes  being  referred  in  each 
case  to  the  volume  of  the  same  body  at  a  standard  temperature. 

When  a  body  exists  in  the  form  of  a  rod  of  bar,  the  length  of 
which  is  to  be  determined  under  different  degrees  of  heat,  the 
increase  of  length  is  called  the  linear  expansion. 

This  is  evidently  not  a  measure  of  the  total  increase  of  vol- 
ume, but  it  is  convenient  in  practice  to  know  the  linear  expan- 
sion as  well  as  the  cubical  expansion. 

70.  The  following  table  gives  the  numbers  by  which  it  is  neces- 
sary to  multiply  the  lengths  of  rods  or  bars  at  32°  Fahrenheit 
in  order  to  find  the  lengths  of  the  same  rods  or  bars  at  212° 
Fahr.     In  other  words,  the  numbers  show  the  increase  of  lengths 
of  rods  of  the  same  substance  for  180°  Fahr.  (from  32°  Fahr.). 
The  proportional  expansion  for  1°  Fahr.  may  be  found  by  divi- 
ding each  number  by  180. 

II.  Table  of  Linear  Expansions  of  Solids. 

Length  at  212°  Fahr. 
of    a  bar  or   rod   the 

NAME  OF  SUBSTANCE.  length  of  which  at  32°  OBSERVER. 

is  1.00000  (unity). 

Glass  tube 1.00082 

Plate-glass 1.00089  Lavoisier  &  Laplace. 

Crowrt-glass 1.00088  "  >               " 

Cast-iron 1.00111  «                 " 

Steel-rod 1.00114  Koy. 

Steel,  tempered  yellow 1.00136  '    Lavoisier  &  Laplace. 

Steel,  tempered  at  light  heat  1.00123  "                " 

Steel  not  tempered 1.00107  "                " 

Soft  iron,  forged 1.00122  "                « 

«       'drawn 1.00123  "                « 

Iron  wire 1.00144  Troughton. 

Bismuth 1.00139  Smeaton. 

2 


18  HEAT. 

Gold,  unannealed 1.00155  Lavoisier  &  Laplace. 

"      annealed 1.00151  "  « 

Copper 1.00172  "  « 

Cast  brass 1.00187  Smeaton. 

Brass  wire 1.00193  " 

Silver 1.00191  Lavoisier  &  Laplace. 

Spelter  solder 1.00205 

Tin 1.00284  Muschenbrock. 

Zinc 1.00296  Smeaton. 

Lead 1.00284  « 

The  above  table  is  taken  from  a  more  comprehensive  table  in 
Watts' s  Dictionary  of  Chemistry,  to  which  the  reader  is  referred 
for  more  complete  information. 

A  complete  table  of  cubical  expansion  for  various  solids  is 
given  also  in  the  same  work ;  such  a  table  is  omitted  here,  be- 
cause for  most  practical  purposes  the  cubical  expansion  or  co- 
efficient of  expansion  of  volume  for  any  substance  may  be  ob- 
tained by  multiplying  the  linear  expansion  given  in  the  above 
table  by  3.  The  coefficients  of  linear  and  cubical  expansion 
thus  found  are  average  values  for  degrees  of  heat  between  32° 
and  212°,  but  these  coefficients  become  slightly  greater  at 
higher  temperatures ;  the  general  rule  being  that  the  coefficient 
of  expansion  increases  the  more  rapidly  as  the  temperature  ap- 
proaches that  which  corresponds  to  the  melting  or  fusing  point. 

71.  Liquefaction,  Melting,  or  Fusion.  —  The  continuous 
transfer  of  heat  to  a  solid,  causing  a  continuous  rise  of  tempera- 
ture and  expansion  of  volume,  produces  ultimately  a  change  of 
aggregation  or  change  of  state  to  the  liquid  form,  called  the 
fusion,  melting,  or  liquefaction  of  the  substance. 

This  law  is  general  for  substances  which  do  not  change 
their  composition  in  changing  their  state.  For  substances 
which  do  not  change  their  composition  the  following  phenom- 
ena ©ccur : 

1.  "  Each  substance  begins  to  melt  at  a  certain  temperature, 
which  is  constant  for  the  same  substance  if  the  pressure  be  con- 
stant." 

2.  u  The  temperature  of  the  solid  remains  at  this  constant 
point  from  the  time  when  fusion  commences  till  it  is  complete." 

3.  "  If  a  substance  expands  in  congelation,  its  melting-point 
is  lowered  by  pressure ;  but  if  a  substance  contracts  in  congeal- 


HEAT.  19 

ing,  its  melting-point  (or  point  of  congelation)  is    raised  by 
pressure."  * 

72.  The  following  table  of  melting-points  in  Falir.  degrees  is 
taken  from  Rankine's  Eules  and  Tables : 

III. 

Mercury -38°  Fahr. 

Ice 32°        " 

Rose's  fusible  metal 210°        " 

(1  part  lead,  1  tin,  2  parts  bismuth.) 

Sulphur 228°  " 

Tin 426°  " 

Bismuth 493°  « 

Lead 630°  " 

Zinc 700°  " 

Silver 1280°?  « 

Brass 1869°?  " 

Copper 2548°?  " 

Gold 2590°?  " 

Cast-iron 3479°,  " 

"Wrought-iron —  higher,  but  uncertain. 

Phosphorus 111°  « 

Wax 147°  " 

The  temperature  at  which  this  change  of  state  occurs  is,  for 
most  substances,  a  fixed  temperature  ;  this  temperature  indicat- 
ing the  limiting  condition  above  which  the  substance  exists  as  a 
liquid,  and  below  which  it  must  exist  as  a  solid. 

73.  The  laws  which  have  been  enunciated  are  subject  to  cer- 
tain qualifications,  such  as  slow  process  of  cooling,  and  variations 
of  external  pressure,  which  may  lower  the  temperature  of  soli- 
dification, but  under  the  same  conditions  they  are  invariable. 

The  continuous  application  of  heat  to  a  solid  at  its  melting- 
point  does  not  raise  its  temperature,  as  long  as  any  portion  re- 
mains solid ;  and,  commonly,  the  abstraction  of  heat  from  a  liquid 
at  its  point  of  solidification,  does  not  lower  its  temperature,  as 
long  as  any  portion  remains  liquid. 

The  change  of  state  is  also  usually  accompanied  by  a  sudden 
change  of  volume. 

Some  substances,  however,  pass  from  the  solid  to  the  liquid 
state  without  showing  a  definite  melting-point,  becoming  plastic 

*  Balfour  Stewart :    Elementary  Treatise  on  Heat,  p.  87. 


20'  HEAT. 

between  these  states.  Glass  and  iron  are  examples,  and  instead 
of  a  definite  melting-point,  a  certain  interval  of  temperature  is 
required  for  the  change. 

74.  Changes  of  Volume  in  Melting. — When  bodies   pass 
from  the  solid  to  the  liquid  state,  the  increased  rate  of  expansion 
is  generally  followed  by  a  further  expansion,  so  that  the  sub- 
stance, after  fusion,  occupies  a  greater  bulk  at  the  same  tem- 
perature than  before  fusion. 

Phosphorus  expands  at  the  moment  of  fusion  about  3.4  per 
cent.,  sulphur  5  per  cent.,  wax  very  slightly,  stearine  about  5 
per  cent. 

Rose's  fusible  metal  exhibits  remarkable  properties  in  this 
respect.  It  is  composed  of  2  parts  of  bismuth,  1  of  lead,  and  1 
of  tin.  When  heated  from  32°  Fahr.  to  about  108°,  it  expands 
in  the  ratio  of  1  to  1.0027 ;  as  the  temperature  is  further  in- 
creased, it  contracts,  its  volume  at  190°  Fahr.  being  the  same  as 
at  32°.  In  melting  it  expands  again,  so  that  at  208°  its  volume 
is  1.01  of  its  volume  at  32°.  This  alloy,  therefore,  contracts 
from  108°  to  its  melting-point  (Watts's  Chemistry). 

Water,  as  is  well  known,  expands  at  the  moment  of  fusion,  or 
contracts  in  melting  about  10  per  cent. ;  one  volume  of  water 
at  32°  Fahr.  gives  1.102  volumes  of  ice,  and  one  volume  of  ice 
.908  volume  of  water  at  the  same  temperature.  Bismuth,  cast- 
iron,  and  antimony  expand  like  water  in  passing  from  the 
liquid  to  the  solid  state. 

75.  Latent  Heat  of  Fluidity. — The  increase  of  the  specific 
heat  of  a  solid,  as  it  approaches  its  melting-point,  appears  to  be 
connected  with  the  increase  of  the  coefficient  of  expansion,  which 
also  increases  simultaneously.     At  the  melting-point  the  whole 
of  the  heat  applied  to  a  body  is  apparently  required  to  overcome 
those  molecular  attractions  which  keep  the  molecules  in  the 
state  of  proximity  belonging  to  the  solid  condition.     The  work 
of  the  heat  applied  is  thus  absorbed  or  expended  without  pro- 
ducing increased  molecular  vibrations. 

Heat  which  would  have  become  sensible  heat  in  the  pure  solid 
or  liquid,  disappears  or  is  transformed  into  the  work  of  overcom- 
ing these  molecular  attractions,  and  is  said  to  become  Latent. 

The  latent  heats  of  fusion  of  a  few  substances,  estimated  in 
units  of  heat,  have  been  determined  experimentally  by  various 
observers,  and  some  of  these  quantities  are  exhibited  in  the 
following  table : 


HEAT.  21 

IY.  Latent  Heats  of  Fusion  of  different  Substances,  according 

to  Person. 

Mercury  ..........  5.086  British  unit  of  heat. 

Phosphorus..  .  .....  9.018  "  " 

Lead  ............  .  9.740  «  " 

Sulphur  ..........  16.954  «  « 

Bismuth  .........  .  22.726  "  « 

Tin  .........  .  ____  25.702  «  « 

Silver  ............  38.057  "  " 

Zinc  ..............  50.682  "  « 

Ice  ...............  140.000  "  « 


76.  Liquids.  —  The  coefficient  of  expansion  of  liquids  with  in- 
crease of  temperature  is  greater  than  that  of  solids,  and,  as  in 
the  case  of  solids,  the  coefficient  increases  with  the  temperature. 

The  coefficient  of  expansion  of  mercury  (i.e.,  the  increase  of 
volume  for*  1°  C.  in  terms  of  the  volume  at  0°,  or  the  melting- 
point  of  ice)  increases  from  0.000179  at  0°  C.  to  .000197  at 
350°  C. 

The  following  table  gives  the  increase  in  volume  of  water 
from  the  experiments  of  Kopp,  taken  from  Balfour  Stewart  : 

Y.  Expansion  of  Wafer  from  0°  Centigrade  to  100°. 

4°  ..........................  1.000000 

10°  ..........................  1.000247 

15°  ..........................  1.000818 

20°  ..........................  1.001690 

30°  ..........................  1.004187 

40°  ..........................  1.007654 

60°  ..........................  1.011890 

60°  ..........................  1.016715 

70°  ..........................  1.022371 

80°  ..........................  1.028707 

90°  ..........................  1.035524 

100°  ..........................  1.043114 

Wlien  cooled  below  4°  Gent.  (39.1  Fahr^  water  expands  by 
a  corresponding  and  nearly  identical  law  for  a  limited  number 
of  degrees. 

In  regard  to  very  volatile  liquids,  like  carbonic  acid,  which 
retains  its  liquid  state  at  ordinary  temperatures,  only  under 


22  HEAT. 

very  great  pressure,  the  coefficient  of  expansion  is  supposed  to 
be  large  relatively.  Tables  of  expansion  for  various  liquids 
may  be  found  in  the  excellent  work  of  Balfour  Stewart,  to 
which  reference  has  already  frequently  been  made. 

The  tables  referred  to  show  that  each  liquid  has  a  coefficient 
of  expansion  different  from  that  of  other  liquids.  To  this  fact 
may  be  added  the  general  law,  that  the  coefficient  of  expansion 
of  the  same  liquid  varies  with  the  temperature  according  to  a 
special  law  for  each  fluid. 

77.  It  may  be  observed,  from  the  tables  of  coefficients  of  ex- 
pansion for  solids  and  liquids,  that  the  total  change  of  volume 
from  the  lowest  to  the  highest  temperature  consistent  with  the 
solid  or  liquid  condition  of  any  substance,  is  very  small  compared 
with  the  actual  volume  of  the  body  which  undergoes  such  a 
change,  and  hence  the  influence  of  the  external  pressure  upon 
the  bounding  surfaces  is  very  slight  during  the  change.  In 
other  words,  the  work  performed  by  heat  in  expanding  liquids 
and  solids  may  be  regarded  as  entirely  expended  in  producing 
change  of  temperature  and  change  of  aggregation,  the  external 
work  in  all  ordinary  cases,  especially  when  the  solid  or  liquid 
is  exposed  only  to  atmospheric  pressure,  being  so  small  that  it 
may  be  disregarded. 

In  the  case  of  bodies  in  the  gaseous  condition,  however,  this 
is  different.  Gaseous  bodies  cannot  exist  in  a  fixed  or  determi- 
nate volume,  ordinarily,  unless  they  are  enclosed  within  bound- 
ing surfaces  or  envelopes. 

The  force  of  cohesion  among  the  particles  of  a  gas  no  longer 
exists  as  in  the  solid  and  liquid  states,  and  the  heat-condition  of 
a  perfect  gas  consists  simply  in  the  oscillation  of  the  molecules, 
(which  is  represented  by  the  actual  temperature  of  the  gas,)  and 
the  outward  pressure  or  repellent  action  of  these  molecules 
which  must  be  resisted  by  the  envelope. 

For  a  definite  volume  of  a  gas  thus  confined,  there  are  thus 
but  two  conditions  involved  in  its  existence :  the  temperature 
and  the  pressure  which  it  exerts  against  the  bounding  surfaces 
of  the  envelope. 

If  such  an  envelope  be  perfectly  elastic  and  heat  be  trans- 
ferred to  the  gas  (the  external  pressure,  such  as  the  pressure  of 
the  atmosphere,  remaining  constant),  the  effect  will  be  an  ex- 
pansion of  volume.  This  expansion  will  be  much  greater  than 
the  expansion  of  liquids  and  solids  for  the  same  increase  of  heat. 


HEAT.    . 


23 


The  coefficient  of  expansion  or  increase  of  volume  under  such 
circumstances,  for  an  increase  of  temperature  of  1°  Fahr.,  has 
been  determined,  through  the  well-known  experiments  of  Reg- 

nault  and  others,  to  be  0.002035  or 


.AM  .  of  the  volume  of  the 
491:4 

Centigrade,  0.00365  or 


of  tne 


gas  at  32°  Fahr.,  and  for  1° 
volume  of  the  gas  at  0°  C. 

If  we  now  compare  the  cubical  dilatation  of  solids,  .liquids, 
and  gases  in  a  general  way,  we  may  take  for  such  comparison 
the  increase  of  volume  from  0°  to  100°  Centigrade. 

78.  The  following  table  is  taken  from  Eankine's  Rules  and 
Tables  : 


VI.  Expansion  for  100°  Centigrade. 


Gases 


0.365 


Liquids. 

Pure  water 0.04775 

Sea-water 0.05 

Spirit  of  wine 0.1112 

Mercury. 0.0182 

Oil,  linseed  and  olive .   0.08 

Solids. 

Brass 0.0065 

Bronze 0.0054 

Copper 0.0055 

Cast-iron.  .    0.0033 


Wrought-iron  and  steel.  0.0036 

Lead 0.0057 

Tin 0.0066 

Zinc 0.0058 

Brick,  common 0.0106 

Fire-brick 0.0015 

Cement 0.0042 

Glass 0.0027 

Slate 0.0031 

Average   Values. 

Solids 0.005 

Liquids 0.060 


The  numbers  under  the  head  Average  Values  exhibit  in  a 
general  way  the  relative  average  expansion  in  bulk  of  solids 
and  liquids,  between  0°  and  100°  C.  or  32°  and  212°  Fahr. 

The  expansion  of  gases,  0.365,  is  strictly  true  only  for  the 
perfect  gases,  i.e.,  gases  which  have  not  been  liquefied. 

In  the  above  comparison  of  the  changes  of  volume  of  solids, 
liquids,  and  gases  under  equal  changes  of  heat,  the  coefficients 
for  solids  and  liquids  are  only  mean  values  between  0°  and  100 
Centigrade. 

And,  moreover,  as  before  remarked,  each  solid  or  liquid  sub- 
stance has  its  own  coefficient,  which  increases  slightly  as  the  tern- 


24  HEAT. 

perature  rises.  In  regard  to  gases,  however,  a  more  simple  law 
holds  true.  The  coefficient  .00365  for  each  degree  Centigrade,  or 
.0020276  for  Fahr.,  is  the  same  for  all  perfect  gases  and  for  all 
pressures  upon  the  external <•  envelope ;  provided  only  that  the 
pressure  be  constant  during  the  change  of  volume  or  during  the 
transfer  of  heat. 

Thus  one  volume  of  a  perfect  gas  at  0°  Cent,  or  32°  Fahr. 
will  become  1-K 0.00365  or  l^-fg-  volume  at  1°  Centigrade  or 
1+0.002035  or  Vh^  volume  at  32° +1°  Fahr. 

A  slight  difference  in  the  coefficients  was  found  by  Regnault 
for  the  different  gases,  and  also  a  slight  difference  at  different 
external  pressures ;  but  for  purposes  of  ordinary  calculation 
the  coefficients  of  all  perfect  gases  may  be  regarded  as  the 
same. 

79.  We  may  conceive,  however,  that  when  heat  is  transferred 
to  a  gas  enclosed  within  an  envelope  (for  instance,  within  a  cylin- 
der which  is  closed  at  one  end  by  a  movable  piston),  the  volume 
and  the  external  pressure  may  change  simultaneously,  and  thus 
the  three  quantities  which  determine  the  condition  of  the  gas, 
viz.,  the  volume  v,  the  pressure  P,  and  the  temperature  t,  may 
all  be  variable  quantities. 

The  relation  between  these  quantities,  under  such  conditions, 
has  been  found,  and  is  represented  by  what  is  well  known  as  the 
law  of  Mariotte  and  Gay-Lussac.  The  following  simple  equa- 
tion is  the  mathematical  enunciation  of  this  law : 

p  v  =  E  (a  + 1) 

in  which  p  is  the  external  pressure  upon  unit  of  surface,  v  the 
volume  of  unit  of  weight,  K  a  constant  which  depends  on  the 
specific  gravity  or  density  of  the  gas  (the  weight  of  this  unit  of 
volume),  t  the  temperature,  and  a  the  number  273,  Centigrade 
degrees  being  employed,  and  459.4:  if  Fahr.  degrees  be  em- 
ployed. 

The  quantity  P,  defined  as  the  external  pressure  upon  a  unit 
of  surface,  is  evidently  also  the  outward  pressure  of  the  gas. 
In  the  illustration  in  which  the  gas  is  supposed  to  be  confined 
in  a  cylinder  with  a  movable  piston,  it  is  apparent  that  when 
there  is  a  state  of  equilibrium,  the  external  and  internal  pres- 
sures must  be  equal.  Hence  the  pressure  P  is  also  called  with 
propriety  the  elastic  force  of  the  gas,  which  is  always  exerted 
in  an  outward  direction. 


HEAT.  25 

80.  Mariotte's  and  Gay-Lussac's  laws  *  combined  are  expressed 
by  the  following  formulas  : 

PV  P0    V0 

2?8+t  =  273+To    ' 
or  PV  PO  v0 


In  this  expression  p  represents  the  pressure  in  pounds  upon 
one  square  foot,  and  v  the  volume  in  cubic  feet  occupied  by 
one  pound  of  the  gas  at  any  temperature  t  (either  Cent,  or 
Fahr.),  PO  v0,  and  t0  represent  respectively  the  pressure,  vol- 
ume, and  temperature  of  the  gas  at  0°  Cent,  or  32°  Fahr. 

"When  absolute  temperatures  are  employed  this  formula  may 
also  be  written  as  follows  : 

PV         P0     V0      ,  P0  V0 

—  —  -  —  -  ;  hence  PV  =  —  -  —  —  x  T 
T  T0  TO 

If  DO  represents  the  density  of  the  gas  at  0°  Cent,  or  32° 
Fahr.,  we  shall  have  v0  =  -  and  substituting  in  the  last  for- 


mula  we  have  — 


P0 

PV  =  —  ~  T 


TO  DO 

For  air  DO  =  .080728  Ibs.,  PO  =  2116.5  Ibs.  and  TO  =  491.4 
Fahr., 

-Z°_  —  E  =  53.354;  hence  P  v  =  K  T  =  53.354  T 
TO  DO 

Again,  if   DO  —  .080728  Ibs.,     PO  =  2116.5   Ibs.  and    TO  = 
273°  Cent. 

^-  =  96.0376  and  P  v  =  RT  =  96.0376  T 
TO  DO 

Since  v  —  --  (i.e.,  one  pound  divided  by  the  weight  of  one 
cubic  foot)  we  can  substitute  and  write  for  air 


p 

—  =  KT 

D 


and  for  any  other  gas, 


*  See  Note  A,  Appendix. 


HEAT. 


Dividing  the  first  of  these  last  two  equations  by  the  second, 
member  by  member,  we  have  — 


i.e.,  the  constants  R  and  R'  are  inversely  proportional  to  the 
corresponding  densities. 

Taking  air  as  a  standard  —  =  s  will  represent  the  specific 

gravity  of  a  gas  whose  density  is  D',  hence 

R  ,     ,        R 

-j-=  s  and  B  =  — 

R  S 

Therefore,  when  the  constant  R  for  air  is  known,  the  constant 
R'  for  any  other  gas  may  be  found  by  dividing  R  by  the  spe- 
cific gravity  s  of  the  gas.  • 

81.  The  following  table  gives  values  of  s  and  R  for  the  sub- 
stances named: 

YII. 

Specific  Gravity.  Values  of  R. 

S  Centigrade.  Fahrenheit. 

Atmospheric  air  ...........   1.00000  96.0376  53.354 

Nitrogen  ..................  97137  98.867  54.926 

Oxygen  ..................   1.10563  86.862  48.257 

Hydrogen  .................  06926  1386.579  770.322 

Steam-gas  (ideal)  (Eankine)  .     .62209  154.379  85.766 

"         "    '   "       (Zeuner)..     .62300  154.153  85.641 

"       saturated   (Zeuner)...     .64000  150.160  83.422 

82.  The  equation  PV  =  R  (459.4  +t)  may  thus  be  applied  to 
any  perfect  gas  whose  specific  gravity  is  known. 

If  in  this  equation  for  the  same  gas  we  suppose  t  to  become 
equal  to—  459.4,  the  second  member  will  become  equal  to  zero, 
and  under  these  circumstances  the  first  member  must  be  zero 
also.  And  as  v  cannot  be  zero  because  the  gas  cannot  be  anni- 
hilated, the  only  supposition  which  will  reduce  the  product  PV 
to  zero  is  that  p  shall  become  zero.  In  other  words,  the  elasti- 
city of  the  gas  disappears. 

This  supposes  that  the  temperature  of  the  gas  has  been  re- 
duced to  the  point  which  has  been  referred  to  as  absolute  cold, 
i.e.,  where  the  heat-motions  or  oscillations  entirely  disappear 
and  the  body  is  without  heat.  The  supposition  that  t  becomes 
at  this  point—  273  on  the  Centigrade  thermometer  and—  459.4 


HEAT. 


27 


Fahr.,  shows  that  this  point  is  far  from  being  beyond  imagin- 
able limits,  although  thus  far  it  has  not  been  practically  realized. 

83.  The  Centigrade  thermometer,  it  is  well  known,  is  an  ordi- 
nary glass-bulb  thermometer,  on  the  stem  of  which  degrees  of 
temperature  are  marked ;  the  melting-point  of  ice  being  0°,  and 
the  boiling-point  of  water  100°,  and  the  interval  being  divided 
into  100  parts  or  degrees.     If  the  graduated  scale  could  be  ex- 
tended downwards  so  as  to  include— 273  of  these  degrees  below 
the  0,  we  should  reach  the  absolute  zero.     In  the  Fahrenheit 
thermometer  the  interval  between  the  melting-point  of  ice  and 
boiling-point  of  water  is  divided  into  180  equal  parts  or  degrees, 
but  each  interval  or  degree  is  thus  smaller  than  the  Centigrade 
degree,  one  degree  of  C.  being  equal  to  1.8  degree  Fahr.,  and 
the  zero  of  the  scale  is  placed  32  degrees  below  the  melting 
point  of  ice. 

84.  To  reduce  Fahrenheit  to  Centigrade,  and  the  reverse,  the 
following  formulae  may  be  used : 


'  9  "  '  1.8 

F.  =  |-  c.  +  32  =  1.8  o.  +  32 

The  following  scale  will  show  the  position  of  the  absolute 
zero  on  these  scales : 


Absolute  Scale. 


Centigrade. 


Fahrenheit. 


Cent. 

400. 

Fahr. 
720  + 

127  + 

260.6 

373. 

300° 

273. 
255. 

200. 
100. 

671  4              +hno  -4- 

212  boiling-point  of  water. 

540°                   4- 

27  + 

80.6 

32  melting-point  of  ice. 
0 

99.4 
279.4 

491.4.  
459.4,  - 

360     — 

0..              ..+ 
17.8........... 

73  - 

180  - 

173...  - 

0. 

0..       - 

273  - 

459.4  absolute  cold. 

28  HEAT. 

These  scales  show  that  the  absolute  temperature  of  any  body 
may  be  found  from  its  temperature  in  Centigrade  degrees  by 
adding  273,  and  for  Fahr.  by  adding  459.4.  Calling  T  the  ab- 
solute temperature  of  a  body,  and  t  the  temperature  on  either 
scale,  the  absolute  temperature  will  always  be 

T  =  273  +  t  for  Centigrade  scale. 
T  =  459.4  +  t  for  Fahrenheit  scale. 

85.  Returning  again  to  the  equation  which  expresses  Mari- 
otte's  law  :  — 

PV  =  R  (459.4  +  t) 

If  we  suppose  the  pressure  or  elasticity  of  the  gas  and  its 
volume  both  to  change  with  a  given  change  of  temperature,  we 
will  have  the  relation  expressed  thus  :  p'v'  =  u  (459.4  +  t)  and, 
dividing  the  first  equation  by  the  second,  member  by  member, 
we  have  — 

PV         459.4  +  t          T         PV  T 

=''  "      <>r 


pV       459.4  +  t'     '   r         p 

Thus  when  absolute  temperatures  are  employed  for  the  same 
gas  we  have  the  ratio  of  the  products  of  the  pressure  by  the  vol- 
ume equal  to  the  ratio  of  the  absolute  temperatures. 

If  the  pressure  remain  the  same  during  a  change  of  volume 

V  T 

and  temperature,  —  7  =  —  r,   that  is,  under  constant  pressure, 

the  volumes  occupied  by  a  given  weight  of  a  perfect  gas  are 
proportional  to  the  absolute  temperatures.  If  the  volumes  re- 
main constant,  as  when  the  gas  is  enclosed  within  a  space  which 

*p  rp 

cannot  change  its  volume,  we  have  —  r  =  —  - 

P  T 

we  also  have  from  the  expression 


_ 

PV  T7 

1  P'     x    T 

v'         P        ~7~ 

This  equation  shows  that  if  the  absolute  temperature  remain 

T 

the  same,  or  -,  =  1,   the  volumes  are  inversely  proportional 
to  the  pressures. 


HEAT.  29 

86.  The  following  problems  will  illustrate  the  use  of  these 
expressions : 

Let  v0  be  the  volume  of  a  given  weight  of  gas  at  0°  C.,  or  at 
32°  Fahr.  (the  melting-point  of  ice),  and  PO  its  elastic  force  at 
the  same  temperature.  Also  let  v1  and  PX  be  the  volume  and 
elastic  force  at  any  absolute  temperature  TI?  and  let  TO  be  the 
temperature  on  the  absolute  scale  of  the  zero  of  the  C.  or  Fahr. 
thermometer  =  273°  C.  or  459.4  +  32  =  491.4  Fahr. 

Then  we  shall  have — 

PO  VQ  =  B  TO 

PQ  Vp  __    _T0 


and  Vl=i_L'.Ji 

PI          TO 

PO    Vp        Tt 
PI   —    ~^       "   TT 


If  P2  and  va  represent  the  elastic  force  and  volume  at  any 
third  absolute  temperature  we  shall  have — 


I    I  _     t 

,  va  ~  '    T2 


and 


If  v  be  the  volume  of  a  unit  of  weight,  as,  for  instance, 
the  volume  of  one  pound  of  the  gas,  or  technically  the  specific 
volume^  we  may  introduce  the  weight  of  a  unit  of  volume, 
or  the  specific  weight,  as,  for  instance,  the  weight  of  a  cubic 
foot. 

If  we  designate  the  weight  of  a  cubic  foot  or  the  density  by 
D,  we  shall  have,  as  has  been  already  stated,  VXD=!,  and  in- 

stead of  v  we  may  substitute  -  '-  in  the  equation  p  v  —  B  T, 
which  will  give 


30  HEAT. 


1 

P   X    -   =  B  T 
D 


and  for  any  other  pressure  and  temperature 

1 

P!  X  —  -  E  T! 
Di 

from  which  may  be  deduced  the  expression 


P!  D      T 

and  D!  = •  — 

p       T! 

from  which  the  density  D!  for  any  absolute  temperature  Tt  may 
be  found  in  terms  of  the  temperature  pressure  and  density  at 
any  other  absolute  temperature. 

87.  In  the  expression  p  v  =  E  T,  if  the  unit  of  surface  be  a 
square  foot,  v  will  represent  a  cubic  foot,  and  if  p  represents  the 
pressure  upon  a  square  inch,  v  will  represent  a  cubic  inch.    The 
pressure  P  may  be  estimated  numerically  in  different  modes, 
either  in  pounds  per  square  foot  or  inch,  or  by  the  height  of  a 
column  of  fluid  of  uniform   density,  the  base  of  which  is   a 
square  foot  or  square  inch. 

88.  In  technical  applications  the  fluids  usually  employed  in 
gauges   for   observing  pressures  are  mercury  and  water,   and 
the  equivalent  values  for  P  in  pounds  in  heights  of  a  column 
of  mercury  and  of  a  column  of  water  will  be  the  height  in  feet 
or  inches  of  a  column  of  these  substances,  which  by  its  weight 
will  give  the   pressure  P,  and  the   ratio   of  the   heights  will 
be  the   same   as   the  ratio  of  the  pressures :  the  simple  rule 
for  any  fluid  being,  that  the  height  of  the  column  multiplied 
by  the  density  of  the  fluid  (or  weight  of  unit  of  volume)  shall 
give  the  numerical  value  of  the  pressure  in  pounds  per  unit  of 
area. 

Tables  of  comparison  of  various  units  may  be  found  in  Ran- 
kine's  Kules  and  Tables,  page  103. 

89.  In  the  expression  p  v  =  E  T,  p  v  indicates  a  condition  of  ac- 
tual energy,  the  pressure  or  elastic  force  arising,  according  to  the 
dynamic  theory  of  heat,  from  the  impact  of  the  heavy  particles 
against  the  sides  of  the  enclosure.     The  values  of  the  quantity 


pv 


=  —  for  the  melting-point  of  ice  for  different  gases  are  given, 


HEAT.  31 

page  26.  These  values  express  in  foot-pounds  the  energy 
exerted  by  one  pound  of  the  different  gases  in  expanding,  at 
constant  pressure,  an  amount  corresponding  to  1°  Fahr.  or  1° 
Centigrade. 

90.  If  a  given  quantity  of  a  perfect  gas.  at  any  temperature 
and  pressure,  be  suddenly  compressed,  the  first  effect,  as  is  well 
known  from  experiment,  is  to  increase  this  energy.  The  vol- 
ume is  diminished  and  the  pressure  increased  in  such  a  manner 
that  P  v  is  at  first  increased,  and  becomes  equal  to  R  T',  T'  being 
greater  than  T.  But  if  the  vessel  in  which  compression  takes 
place  be  allowed  to  stand  for  some  time,  the  product  returns  to 
its  original  value,  R  T.  The  heat  generated  by  the  work  of  com- 
pression being  dissipated,  the  actual  energy  remains  as  it  was 
before,  and  it  might  be  supposed  that  all  the  work  of  compres- 
sion has  been  lost.  But  while  the  value  of  the  product  P  v  has 
not  changed,  the  separate  factors  have  changed,  P  becoming 
greater  and  v  smaller,  and  the  gas  has  assumed  a  new  condition 
of  potential  energy  compared  with  its  former  condition.  In 
this  respect  it  acts  like  a  spring  which  has  been  compressed 
and  held  in  place  by  a  constant  force.* 

If  a  gas  be  allowed  to  expand  suddenly  by  a  reduction  of 
external  pressure,  the  heat  which  was  dissipated  is  not  restored, 
and  a  loss  of  work  occurs.  This  is  the  actual  occurrence  in 
engines  which  utilize  compressed  air.  The  work  performed  by 
the  expansion  is  performed  at  the  expense  of  the  heat  of  the 
gas  or  air  itself,  and  its  final  temperature  is  restored  only  after 
it  passes  away  from  the  engine,  involving  a  loss. 

If  the  expansion  could  take  place  under  such  circumstances 
that  the  heat  which  was  dissipated  after  the  compression  (due 
to  the  work  of  compression)  could  be  restored  by  a  natural  pro- 
cess from  the  surrounding  bodies  to  which  it  was  imparted, 
no  loss  would  occur.  This  condition  is,  however,  impracti- 
cable. 

91.  The  relations  which  subsist  between  the  temperatures, 


*  The  elastic  force  of  a  spring  is  not  dissipated,  but  acts  promptly  and  sud- 
denly when  the  force  which  retains  it  is  removed.  Compressed  gas  acts  in  the 
same  manner,  except  that,  to  be  restored  to  the  same  condition  as  before  the 
compression,  performing  work  equal  to  the  work  of  compression,  all  the  heat 
which  was  dissipated  must  be  restored  by  surrounding  bodies — a  process  which 
requires  time  ;  and  therefore  a  compressed  gas  is  not  a  true  reciprocating  force 
in  machinery. 


32  HEAT. 

pressures,  and  volumes  of  a  perfect  gas  have  been  considered 
under  the  suppositions  that  these  quantities  are  respectively 
constant  in  succession. 

It  is  often  necessary  to  discuss  problems  the  conditions  of 
which  require  all  three  of  these  quantities  to  vary  simulta- 
neously. In  the  case  just  presented,  the  compression  of  air, 
and  the  subsequent  utilization  of  it  as  a  source  of  energy  in  an 
engine,  such  conditions  are  presented. 

The  compression  may  take  place  in  such  a  manner  that 
during  the  compression  the  temperature  of  the  gas  or  air  is  in- 
creased, or  it  may  take  place  in  such  a  manner  that  the  tem- 
perature remains  constant,  as  when  a  current  of  cold  water 
is  used  freely  to  abstract  the  heat.  In  all  cases  the  final  tem- 
perature usually  returns  to  the  original  temperature,  and  the 
problem,  as  far  as  pressure  and  volume  are  concerned,  is  a 
simple  one,  following  the  law  that  the  volumes  are  inversely 
as  the  pressures.  The  quantity  of  heat  evolved  will  be  the 
exact  equivalent  of  the  external  work  performed. 

Applying  the   fundamental   expression   for  perfect    gases, 

A   +   C 


In  this  case  the  term  A,  which  denotes  loss  or  gain  of  living  force, 
is  zero,  because,  in  the  final  state  of  the  gas,  the  temperature 
which  represents  the  vis  viva  due  to  the  molecular  motions  is 
unchanged.  The  work  c  is  negative,  and  the  equation  reduces  to 


-o  c 


or  Q  = 


772  w  •  772 
conversely,  where  heat  is  transferred  to  a  gas  all  the  heat  will 
be  transformed  into  external  work  when  a  given  quantity  of  a 
perfect  gas  passes  from  one  state  of  equilibrium  to  another,  and 
when  the  temperatures  of  the  two  limiting  states  are  the  same, 
whatever  be  the  mode  of  expansion. 

In  an  engine,  however,  the  expansion  takes  place  suddenly,  and 
there  is  a  depression  of  the  temperature  of  the  gas,  if  no  heat 
be  transferred  to  it,  and  the  work  performed  by  an  expanding 
gas  under  these  circumstances  will  depend  upon  the  relations 
between  p,  v  and  T. 

These  relations  are  expressed  by  the  following  equations : 

-IW^V     and       -*L  =  (^^' 


HEAT.  33 

from  which  are  deduced 


l 


in  which  K  is  the  ratio  of  the  specific  heat  of  a  perfect  gas  under 
constant  pressure  to  its  specific  heat  under  a  constant  volume. 
For  air  the  ratio  of  the  apparent  to  the  real  specific  heat  is 
equal  to 

A  =  1,408 

/ ..  >, 
the  values  of  the  exponents  will  then  be  numerically 

k      =  1.408  k_  =  3.451 

k-1 
k-1  =     .408  Jl^  =     .71 

k 

JL_  =  2.451  k-1  =     .29 

k-1  k 

The  work  of  expansion  and  the  heat  lost  by  the  gas  in  units 
:  work  will  be  expressed  by 


— r  — 

of  work  will  be  expressed  by 

Q  x  772  =  w  = 


VAPORS. 

92.  It  is  well  known,  from  common  observation,  that  many 
liquids,  such  as  water,  alcohol,  and  ether,  if  not  confined  in 
close  vessels,  become  transformednnto  a  condition  resembling 
the  gaseous  condition  at  ordinary  temperatures,  and  disappear 
as  liquids,  being  diffused  in  the  atmosphere  as  vapors.  This 
transformation  takes  place  in  nearly  all  liquids  more  or  less 
rapidly  at  ordinary  temperatures,  though  for  some  no  such 
transformation  takes  place  at  very  low  temperatures.  It  is  con- 
sidered probable,  however,  that  this  quiet  change  takes  place  in 
all  liquids  above  certain  fixed  temperatures.  Many  solids,  also, 
3 


34  HEAT. 

e.g.,  ice  and  camphor,  pass  to  the  state  of  vapor  without  passing 
through,  the  intermediate  liquid  state,  under  certain  conditions. 

If  a  closed  vessel  be  partly  filled  with  a  liquid,  the  space 
above  the  liquid  will  thus  ordinarily  become  filled  with  the 
vapor  of  the  liquid,  and  the  elastic  force  of  the  vapor  will  de- 
pend on  the  nature  or  kind  of  liquid,  the  volume  of  the  enclosed 
space,  and  the  temperature.  If  heat  be  applied  to  the  liquid 
in  this  condition,  the  formation  of  vapor  will  continue,  the 
vapor  exerting  a  certain  additional  elastic  force  depending  on 
the  temperature  alone,  as  long  as  there  remains  any  liquid. 
Evaporation  will  cease  when  the  application  of  heat  is  suspend- 
ed, and,  if  the  liquid  be  cooled,  condensation  will  occur ;  so 
that  the  relative  quantities  of  liquid  and  vapor,  and  the  elastic 
force  of  the  latter,  in  a  given  space  and  for  a  given  liquid,  are 
dependent  on  the  condition  of  heat  or  temperature  solely. 

.Similar  phenomena  will  follow  if  the  extent  of  the  enclosed 
space  be  enlarged  or  contracted,  the  temperature  remaining 
the  same.  If  the  space  be  enlarged,  an  additional  quantity  of 
the  liquid  will  pass  into  the  state  of  vapor ;  and  if  the  space  be 
contracted,  a  certain  amount  of  the  vapor  will  be  reconverted 
into  liquid. 

93.  For  every  liquid  in  an  enclosed  space  there  is  thus  a  cer- 
tain tension  or  elastic  force  depending  on  the  temperature  (what- 
ever be  the  relative  volumes  of  the  liquid  and  the  free  space 
above  it)  which  is  the  greatest  elastic  force  that  the  vapor  can 
have  at  each  particular  temperature.     If  the  vapor  be  com- 
pressed, liquid  is  formed  by  condensation,  and  if  the  space  be 
enlarged,  or  the  external  pressure  which  confines  the  vapor  be 
diminished,  additional  vapor  will  be  formed,  and  the  elastic 
force  will  remain  thus  constant  for  each  constant  temperature. 

94.  A  vapor  in  this  condition  in  presence  of  its  liquid  is  said 
to  be  saturated.     Properly  speaking,  it  is  the  space  which  is 
saturated,  i.e.,  it  contains  the  greatest  quantity  of  vapor  possible 
at  the  given  temperature. 

95.  This  law  of  vapors,  viz.,  that  the  plastic  force  in  a  given 
volume  depends  solely  on  the  temperature,  is  approximately 
true,  whether  the  space  in  which  the  vapor  is  formed  be  va- 
cuous, or  whether  it  contain  air  or  any  other  permanent  gas, 
provided  that  the  liquid  exerts  no  solvent  or  chemical  action  on 
the  gas. 

96.  The  combined  elastic  forces,  or  the  resultant  pressure  on 


HEAT.  35 

the  sides  of  the  vessel,  when  a  permanent  gas  is  present  which 
is  not  acted  upon  by  the  liquid,  is  nearly  the  sum  of  the  elastic 
force  of  the  gas,  and  the  maximum  tension  of  the  vapor  at  the 

O          "  I 

given  temperature.  It  was  found  by  Itegnault,  in  experiments 
on  this  subject,  that  liquids  do  not  give  off  vapor  of  quite  so 
great  a  tension  in  a  space  occupied  by  a  permanent  gas  as  they 
do  in  a  vacuum,  and  that  the  difference  increases  as  the  tem- 
perature rises  ;  but  for  technical  applications,  under  ordinary 
temperatures,  the  law  may  be  considered  true. 

The  only  difference  between  evaporation  in  a  vacuum  and  in 
a  space  occupied  by  a  gas  is,  that  the  formation  of  vapor  takes 
place  more  slowly,  if  a  gas  be  present,  a  fact  of  great  import- 
ance in  the  economy  of  nature  connected  with  the  evaporation 
of  water  from  the  surface  of  the  earth. 

97.  When  heat  is  continuously  applied  to  a  liquid  in  a  closed 
vessel,  the  space  enclosed  remaining  constant,  the  temperature 
of  the  liquid  and  vapor  will  continually  increase  if  there  be  no 
dissipation  of  heat  through  the  sides  of  the  vessel ;  the  quantity 
of  the  liquid  will  diminish  and  the  pressure  will  increase,  the 
vapor  remaining  saturated  as  long  as  any  liquid  remains.  After 
the  last  element  of  liquid  shall  have  passed  to  the  state  of  vapor, 
if  heat  be  still  applied  the  vapor  begins  to  assume  the  proper- 
ties of  the  permanent  gases.     Under  this  condition,  if  the  tem- 
perature could  be  indefinitely  raised,  or  the  volume  of  the  space 
indefinitely  increased,  under  a  constant  temperature,  the  vapor 
would  finally  arrive  at  a  state  corresponding  to  that  of  perfect 
gas,  and  would  then  follow  strictly  the  law  of  Mariotte  and  Gray- 
Lussac ;  and  hence  it  may  be  said  that  the  physical  properties 
of  vapors,  when  sufficiently  expanded  or  at   sufficiently  high 
temperatures,  and  when  they  are  not  in  contact  with   their 
liquids,  are  identical  with  those  of  perfect  gases. 

98.  Complete  Vaporization. — The  temperature   at  which 
the  complete  evaporization  of  a  liquid  in  a  given  space  will  oc- 
cur depends  on  the  relative  volumes  of  the  liquid  and  the  space 
above  it.     With  alcohol,  the  empty  space  being  about  equal  to 
that  occupied   by  the  liquid,  complete  vaporization  takes  place 
at  about  400°  Fahr.     In  the  case  of  water,  if  the  space  occu- 
pied by  the  water  be  about  one-fourth  of  the  whole  internal 
volume  of  the  vessel,  the  liquid  will  be  wholly  converted  into 
vapor,  if  the  vessel  be  strong  enough  to  resist  the  pressure,  at 
about  680°  Fahr.     (Cagniard  de  la  Tour.) 


36  HEAT. 

99.  The  tension  of  the  vapors  of  mixed  liquids,  as  determined 
by  Regnault,  is  the  sum  of  the  tensions  of  the  two  vapors  taken 
separately,  if  the  liquids  have  no  solvent  action  on  each  other. 
With  water  and  ether,  the  tension  of  the  vapor  of  the  mixture 
is  less  than  that  of  the  sum  of  the  tensions  of  the  two  liquids 
taken  separately,  being  hardly  equal  to  that  of  ether  alone. 
When  two  liquids  dissolve  each  other  in  all  proportions,  e.  g. 
water  and  alcohol,  the  resultant  tension  is  intermediate  between 
the  tensions  of  the  separate  liquids. 

100.  Boiling-Points. — The  boiling-point  of  a  liquid  is  an  ex- 
pression which  usually  refers  to  a  fixed  or  standard  pressure 
upon  the  exterior  surface,  the  pressure  of  the  atmosphere  ;  and 
it  indicates  the  temperature  at  which  the  elastic  force  of  the 
vapor  is  equal  to  such  standard  pressure. 

101.  Ebullition  is  a  phenomenon  which  takes  place  when 
heat  is  applied  to  the  lower  part  of  the  mass  of  a  liquid  which 
has  been  heated  to  the  boiling-point,  and  arises  from  the  forma- 
tion of  bubbles  of  vapor  at  the  point  at  which  the  heat  is  ap- 
plied, the  bubbles  rising  through  the  liquid  and  escaping  at  the 
free  surface. 

The  formation  of  such  bubbles  may  occur  before  the  whole 
mass  of  the  liquid  has  been  heated  to  the  boiling-point,  but  in 
this  case  the  bubbles  are  usually  condensed  before  they  reach 
the  surface. 

102.  " Boiling-Point  due  to  the  Pressure" — is  an  expres- 
sion sometimes  employed  to  designate  the  temperature  corre- 
sponding to  the  pressure,  whether  that  temperature  be  above  or 
below  the  standard  temperature  for  which  the  boiling-points  of 
the  tables  are  determined. 

The  following  are  the  boiling-points  of  a  few  of  the  liquids  or- 
dinarily met  with,  under  atmospheric  pressure,  in  degrees  Fahr. : 

VIII.  Water 212° 

Ether 96° 

Alcohol 173° 

Sulphur 601° 

Sulphuric  acid 630° 

Mercury 660° 

Acetic  acid 243° 

103.  The  boiling-point  of  a  liquid,  under  any  pressure,  is, 
properly  speaking,  the  lowest  temperature  at  which  ebullition 


HEAT.  37 

can  occur,  since  there  may  be  circumstances  under  which  ebul- 
lition, or  the  formation  of  vapor,  does  not  take  place  until  the 
liquid  has  been  heated  many  degrees  above  its  tabulated  boil- 
ing-point. 

If  the  free  surface  of  a  liquid  be  covered  or  surrounded  by 
another  which  has  a  higher  boiling-point,  the  bubbles  of  vapor 
of  the  interior  liquid  having  no  escape,  this  liquid  may  attain 
a  temperature  higher  than  its  ordinary  boiling-point. 

It  was  found  by  Dufour  that  globules  of  water  suspended  in 
oil  could  readily  be  heated  to  27°  Fahr.  above  the  boiling-point 
under  atmospheric  pressure,  and  the  vaporization  of  the  bubble 
was  then  accomplished  only  by  contact  with  some  solid  body 
which  caused  a  sudden  evaporation.  In  some  experiments  on 
very  minute  bubbles  of  wrater,  he  succeeded  in  heating  the 
liquid  to  178°  C.,  or  352°  Fahr.,  a  temperature  corresponding  to 
a  pressure  of  9  atmospheres. 

Prof.  Donny,  of  Ghent,  observed  that  water  thoroughly  de- 
prived of  air  and  sealed,  up  in  a  long  glass  tube  at  atmospheric 
pressure  could  be  heated  to  138°  C.,  or  280°  Fahr.,  a  tempera- 
ture corresponding  to  3.5  atmospheres.  The  evaporation  was 
then  sudden,  and  the  water  was  violently  thrown  to  the  opposite 
end  of  the  tube.  (Watts's  Chemistry.) 

The  retardation  of  ebullition  in  alkaline  solutions  is  £  pheno- 
menon often  observed. 

104.  The  boiling-points  of  liquids  are  also  influenced  by  the 
nature  of  the  vessel.     Water  has  generally  a  higher  boiling- 
point  by  several  degrees,  under  atmospheric  pressure,  in  glass 
vessels  than  in  iron  vessels. 

105.  Liquids  holding  solid  bodies  in  solution  generally  boil  at 
higher  temperatures  than  when  .the  liquid  is  pure.    The  boiling- 
point  of  saturated  brine  at  atmospheric  pressure  is  about  226° 
Fahr.     As  a  rule,  it  is  considered  that  a  saline  solution,  sea- 
water,  for  instance,  has  its  boiling-point  raised  1.2°   Fahr.  for 
each  -£%  of  salt  that  the  water  contains.      Average  sea -water 
contains  about  •£%• ;    and   the  brine  in  marine   boilers  is  not 
allowed  to  be  concentrated  more  than  -f%  to  ^  as  determined 
by  a  salinometer.      It  was  found  by  Magnus  that  the  tempera- 
ture also  of  the  vapor  of  saline  solutions  is  higher  than  that  of 
the  vapor  of  pure  water  under  the  same  pressure,  the  difference 
being  greater  as  the  solution  becomes  more  concentrated. 

106.  Nebulous  or  vesicular  vapor  is  that  which  arises  from  the 


38  HEAT. 

condensation  of  particles  of  a  vapor  in  the  atmosphere,  or  in  its 
own  vapor,  constituting  cloud  or  mist.  If  heat  be  applied  to 
vesicular  vapor  the  condensed  globules  evaporate  and  the  vapor 
becomes  transparent,  though  still  saturated.  If  heat  be  ab- 
stracted, new  particles  are  condensed ;  the  globules  coalesce  and 
fall  in  drops. 

107.  Superheated  Vapor. — When  a  vapor  at  the  point  of 
saturation  is  removed  from  contact  with  its  liquid  and  heated,  it 
is  said  to  be  superheated. 

A  saturated  vapor,  not  in  contact  with  its  liquid,  may  become 
superheated  by  the  enlargement  of  the  space  which  contains  it ; 
for  it  will  then  admit  of  compression  without  condensation,  and 
will  have  a  pressure,  at  the  same  temperature,  inferior  to  that  of 
saturated  vapor,  and  also  a  temperature  more  elevated  than  that 
due  to  saturation  for  the  same  pressure.  If  S  represent  the 
weight  of  unit  of  volume  (the  density),  and  Y  the  volume  of 
unit  of  weight,  it  is  evident  that  at  the  point  of  saturation  S  has 
its  maximum  and  Y  its  minimum  value. 

Yapors  may  be  superheated  to  some  extent,  even  when  some 
part  of  the  volume  of  the  vapor  is  in  contact  with  its  liquid,  by 
a  sudden  transfer  of  heat  to  the  vapor,  if  the  conditions  are  such 
that  this  heat  is  but  slowly  conducted  to  the  liquid.  Steam  may 
thus  be  superheated  in  pipes  the  lower  parts  of  which  are  filled 
with  water ;  or  in  the  dome  or  steam-chamber  of  a  boiler.  It  is 
evident,  however,  that  this  is  not  a  condition  of  equilibrium, 
and  that,  as  heat  reaches  the  liquid  by  conduction,  new  parti- 
cles of  vapor  will  be  formed,  if  the  process  of  superheating  be 
suspended. 

108.  Spheroidal  State. — It  is  a  matter  of  common  observa- 
tion that  when  water  is  sprinkled  upon  the  horizontal  flat  sur- 
face of  a  hot  stove,  the  drops  are  not  immediately  converted  into 
steam,  but  roll  about  on    the   heated  surface,  and  gradually 
evaporate,  retaining  all  the  time  the  spherical,  or  spheroidal 
(flattened  sphere)  form.    This  condition  is  not  peculiar  to  water, 
but   may   be    experimentally   demonstrated   with   all   volatile 
liquids,  and  is  usually  described  as  the  sphero'idal  state.   It  arises 
from  the  fact  that  the  rapid  formation  of  vapor  makes  a  layer  or 
bed  of  vapor  on  which  the  drop  rests,  and  which  prevents  actual 
contact  between  the  drop  and  the  surface.     The  phenomenon 
may  occur  also  whether  the  heated  surface  be  liquid  or  metallic, 
the  condition  being  that  the  surface  shall  be  heated  to  a  point 


HEAT.  39 

considerably  above  the  boiling-point  of  the  liquid  drop.  Experi- 
ments by  Boutigny  showed  that  the  lowest  temperature  at  which 
a  metallic  vessel  will  cause  the  spheroidal  state  is  289°  F.  for 
water,  273°  F.  for  alcohol,  and  141°  F.  for  ether.  The  sphe- 
roidal condition,  sometimes  called  "  Leidenfrost's  Phenomenon," 
illustrates  an  important  fact  in  regard  to  the  transfer  of  heat, 
which  will  be  treated  of  in  a  subsequent  chapter.  It  shows  that 
for  the  rapid  transfer  of  heat  to  a  liquid  there  must  be  actual 
liquid  contact  with  the  heated  surface — the  interposition  of  a 
thin  film  of  gas  acting  as  an  obstruction  to  the  passage  of  heat. 

109.  Humid  Vapor. — The  vapor  of  water  which  is  usually 
employed  in  industrial  operations  usually  contains  particles  of 
water  mechanically  suspended  in  the  vapor.     The  steam  is  then 
not  only  saturated  but  wet.      When  in  the  simple  condition  of 
saturated  vapor,  it  is  called  dry  steam. 

110.  Steam-gas  is  a  term  applied  by  some  writers  to  super- 
heated steam,  or  steam  in  the  condition  of  a  perfect  gas. 

Expansion  of  Dry  Saturated  Steam. — If  dry  saturated 
steam  be  enclosed  in  a  vessel,  and  the  volume  be  enlarged  by 
extending  the  space  in  such  a  manner  that  the  elastic  force  of 
the  steam  performs  no  work,  the  steam  will  become  superheated, 
i.e.,  its  temperature  will  be,  at  the  end  of  the  expansion,  higher 
than  that  due  to  the  boiling-point  corresponding  to  the  pres- 
sure, and  it  will  remain  transparent. 

If,  however,  the  expansion  takes  place  against  a  pressure  so 
that  there  is  work  performed  by  the  elastic  force,  condensation 
of  a  portion  of  the  steam  will  take  place,  and  the  mass  of  steam 
will  present  a  cloudy  appearance.  This  fact  was  determined 
theoretically  by  Rankine  and  by  Clausius,  and  experimentally 
by  Him.  It  is  supposed  that  no  heat  is  communicated  to,  or 
abstracted  from,  the  vapor  during  the  expansion.  This  con- 
densation does  not  take  place  in  steam  sufficiently  superheated. 

From  the  experiments  of  Fairbairn  and  Tate  on  superheated 
vapors,  it  appears  that  for  an  interval,  of  about  18°  Fahr.  above 
the  temperature  due  to  the  pressure,  the  coefficient  of  expansion 
of  a  superheated  vapor  is  greater  than  that  of  perfect  gases,  but 
above  this  temperature,  the  relation  between  the  volume  and 
pressure  follows  closely  the  law  of  Mariotte.  It  is  con- 
tended by  Morin  and  Tresca  (Des  Machines  d  Vapeur)  that  the 
law  of  Mariotte,  viz.,  i»  v  =  constant,  may  in  all  cases  be  ap- 
plied to  the  expansion  of  dry  saturated  steam  without  great 


4:0  HEAT. 

error,  and  that  the  weight  of  a  cubic  metre  of  vapor  may  always 
be  taken  at  0.622  of  that  of  air  at  the  same  temperature  and 
pressure.  Clausius  demonstrated,  on  the  contrary,  that  this  law 
is  only  approximate,  unless  the  vapor  be  considerably  removed 
from  its  point  of  condensation  —  a  conclusion  which  seems  to  be 
fully  confirmed  by  the  latest  investigations,  especially  those  of 
Prof.  Zeuner. 

111.  Specific  Heats  of  Gases  and  Vapors.  —  The  specific 
heat  of  a  substance  has  already  been  referred  to  as  the  quantity 
of  heat,  in  units  of  heat,  necessary  to  cause  a  change  of  1°  in 
the  temperature  of  one  unit  of  weight  of  the  substance  at  some 
standard  temperature  and  pressure. 

A  standard  temperature  and  pressure  are  necessary,  because 
the  specific  heats  of  all  substances,  except  perfect  gases,  vary 
slightly  with  the  external  pressure  and  with  the  temperature. 
The  unit  of  heat  in  English  measures  to  which  other  special 
units  or  specific  heats  are  referred,  has  been  defined  to  be  the 
quantity  of  heat  necessary  to  cause  a  change  of  1°  in  1  pound  of 
pure  water  at  the  temperature  of  39°.l  Fahr.,  and  the  specific 
heats  of  the  tables  are  expressed  in  fractions  of  the  unit  of  heat. 

The  expression  — 

Q  = 


which  illustrates  the  effect  of  a  change  of  heat  Q  in  any  sub- 
stance, solid,  liquid,  or  gaseous,  shows  that  a  quantity  of  heat 
added  to  a  given  quantity  of  any  substance  causes  these  effects, 
as  has  been  already  stated,  viz.  :  increase  of  molecular  vibra- 
tion, or  increase  of  sensible  heat,  represented  by  A  ;  change  of 
position  of  the  particles  (overcoming  forces  of  attraction),  B  ; 
and  overcoming  external  pressure,  c,  arising  from  expansion  or 
increase  of  volume. 

From  this  it  appears  that  the  change  of  sensible  heat  repre- 
sented by  A  does  not  include  all  of  the  heat  involved  in  the 
change  ;  and  the  thermometer  will  give  only  an  apparent  spe- 
cific heat  —  the  real  specific  heat  being  the  whole  heat,  part  of 
which  has  been  expended  in  producing  the  effects  B  and  c,  re- 
presenting internal  and  external  work,  and  which  has  disap- 
peared as  heat. 

If  the  substance  can  be  confined  to  a  constant  volume,  it  is 
evident  that  these  terms  will  vanish,  and  the  apparent  will  be 
also  the  real  specific  heat. 


HEAT.  4-1 

In  solids  and  liquids  the  amount  of  expansion  is  so  small 
that  the  difference  between  the  real  and  apparent  specific 
heats  is  small.  Nevertheless,  it  exhibits  itself  in  experiments 
for  determining  specific  heats,  by  showing  an  increase  of  spe- 
cific heat  as  the  expansion  increases. 

The  following  tables  illustrate  this  fact. 

If  the  mean  specific  heat  is  taken  between  32°  and  212°,  they 
will  be  as  shown  in  the  first  column  ;  and  if  between  32°  and 

540°  Fahr.,  the  results  are  given  in  the  second  column. 

\ 

IX.  Specific  Heats. 

Mean  bet.  32  and  212.        Mean  bet.  32  and  540. 

*  Iron  ......................  0.109  0.1218 

Mercury  ..................  0.0330  0.0350 

Zinc  ......................  0.0927  0.1015 

Antimony  .................  0.0507  0.0549 

Silver  .....................  0.0557  0.0611 

Copper  ....................  0.0949  0.1013 

Platinum  ........  ..........  0.0355  0.0355 

Glass  ...........  ..........  0.1770  0.1990 

For  water,  the  increase  of  specific  heat  is 

•(•  o  =  spec,  heat  =  1.  at  0  Centigrade. 

=  1.0042   at  50°  Centigrade. 
=  1.0132    "   100°         " 
=  1.0262    «   150°        « 
=  1.0440    "   200°         " 
=  1.0568    "   230°         " 

For  gases  it  has  been  explained  that  the  term  B  disappears 
(being  the  work  of  overcoming  the  forces  of  attraction  when 
the  volume  is  increased),  and  the  expression  above  reduced  to 


If  now  the  gas  be  kept  at  constant  volume,  no  expansion  will 
occur,  and  the  term  c  will  also  disappear,  and  the  whole  effect  of 
a  transfer  of  heat  to  the  body  will  be  to  cause  an  increase,  A. 
But  if,  in  addition  to  the  same  change  in  A,  the  gas  expands 
and  performs  work  represented  by  o,  the  specific  heat  will  be 
greater.  This  is  called  the  apparent  specific  heat  of  the  gas,  and 
the  specific  heat  under  constant  volume  the  real  specific  heat. 

*  Balfour  Stewart.  f  Wurtz,  Die.  de  Chemie. 


42  HEAT. 

112.  The  .results  of  experiments  by  Regnault  to  determine  the 
specific  heats  of  gases  at  constant  pressure  are  given  in  the 
following  table  for  the  substances  named : 

Name  of  Substance.  Specific  heats  at  constant  pressure. 

X.  Air 0.2377 

Oxygen 0.2182 

Nitrogen 0.2440 

Hydrogen 3.4046 

Carbonic  Acid 0.2164 

Carbonic  Oxide 0.2479 

Marsh  Gas 0.5929 

Ammonia 0.5080 

Sulphuric  Acid 0.1553 

113.  For  specific  heats  of  gases  at  constant  volume  direct  ex- 
periments are  difficult,  and  they  have  been  determined  only  by 
indirect  methods. 

Let  c  be  the  specific  heat  of  a  gas  at  constant  pressure,  and 
c'  the  specific  heat  at  constant  volume :  the  value  of  the  ratio 

f~\ 

- ,  may  be  determined  by  various  methods.    The  results  of  these 

C 

c\ 

methods  indicate  that  for  air  the  ratio  is  —.  =  1.410  =  k,  the 

o 

exponent  employed  in  the  formulae  given  for  the  expansion  of 
gas  in  a  previous  paragraph. 

For    steam   in   the    perfectly   gaseous   state,   according    to 

Rankine  the  ratio  is  -,=1.304,  arid  according  to  other  writers 
5=1.333. 

o 

The  specific  heat  of  air  under  constant  volume,  found  in  this 
manner,  is  0.169. 

The  difference  between  0.2377,  the  specific  heat  at  constant 
pressure,  and  0.169=0.069,  is  really  the  latent  heat  of  expan- 
sion of  air  for  1°  at  32°. 

114.  By  comparing  the  work  due  to  the  expansion  of  air  in 
foot-pounds  with  this  quantity  0.069,  a  theoretical  verification  of 
the  mechanical  equivalent  of  heat  may  be  found. 

Let  one  pound  of  air  be  subjected  to  a  change  of  heat  cor- 
responding to  1°  Fahr.,  first  under  constant  pressure,  and  sec- 
ond under  constant  volume. 


HEAT.  43 


A-f-C 

According  to  the  expression  Q=  -    —which  represents,  gene- 

E, 

rally,  the  dynamic  conditions  of  the  problem,  and  in  which  E 
represents  the  dynamic  equivalent  of  heat,  we  shall  have,  in 
the  first  case  — 


and  in  the  second,  since  o  disappears,  being  the  work  due  to 
expansion,  we  have  — 


and  (Q—  Q)  E—  A  —  A-f-c=c 

Q—  Q!  is  the  difference,  in  units  of  heat,  between  the  quan- 
tities of  heat  necessary  to  raise  one  pound  of  air  1°  under  the 
conditions  of  constant  pressure  and  constant  volume,  and  will 
be  represented,  according  to  the  corresponding  values  of  the 
specific  heats,  by 

0.069  x  1°  units  of  heat, 
and  we  shall  have  — 

0.069  x  1°  x  E=c=work  of  expansion. 
But  we  have  from  Mariotte  and  Gay-Lussac's  law 

pv=53.35T 
and  pv'=53.35T' 

and  P  (v-v')=53.35  (T~T')=53M  xl° 

But  P,  the  external  pressure,  x  by  the  change  of  volume,  is  the 
work  of  expansion  =  a 

Hence  c=53.35xl° 

0.069  xl°xE=53.35xl° 
0.069  xE=53.35 
53.35 


This  is  a  theoretical  dynamic  equivalent  of  heat,  depending 
on  the  law  of  Mariotte  and  Gay-Lussac,  and  the  values  of  spe- 
cific heats  found  by  experiment. 

Actual  direct  determinations  of  this  equivalent  have  been 
made  by  different  investigators,  with  the  results  given  below  : 


4A  HEAT. 

Dynamic  Equivalent. 

V.    Kegnault,    Moll 

and  V an  Beck  . .  .Experiments  on  Air  .....  768.6 

Joule. Friction  of  Water .  772.69 

"     Friction  of  Mercury 774.08 

"     "        "Cast  Iron 774.99 

Favre Friction 

Him Work  of  Steam  Engine. . .  752.8 

Joule Heat  Evolved  by  Electro- 
Magnetic  Engine 823.6 

The  number  772.69,  determined  by  Joule,  is  regarded  as  the 
most  satisfactory,  and  772  has  been  adopted  as  the  equivalent 
in  English  measures,  and  is  often  called  Joule's  Equivalent. 
Compared  with  the  above  theoretical  determination,  we  have — 

Theoretical E=773.2 

Experimental  by  Joule E— 772.69 


Difference. 0.51  foot-lb. 

The  specific  heats  of  the  vapors  of  water,  alcohol,  and  ether, 
as  determined  by  Regnault,  are  given  in  the  following  table, 
together  with  the  densities  at  32°,  and  .at  one  atmospheric  pres- 
sure : 

Density— air  being  unity.        Specific  heat. 

Yapor  of  Water 0.622 0.4750 

"       Alcohol 1.589 0.4513 

"       Ether 2.556 .... 0.4810 

115.  In  regard  to  the  specific  heats  of  bodies,  it  is  maintained 
by  Clausius  that  the  true  or  real  specific  heat  of  a  body  would 
be  constant  if  the  volume  were  kept  constant  for  all  states,  solid, 
liquid,  and  gaseous. 

Rankine  maintains,  on  the  other  hand,  that  the  real  specific 
heats  remain  constant  if  there  is  no  change  of  volume,  only  so 
long  as  the  substance  retains  the  same  state,  solid,  liquid,  or 
gaseous ;  and  that  a  change  of  specific  heat  occurs  with  a 
change  of  state,  even  though  there  is  no  change  of  volume.  It 
is  difficult  to  decide  such  a  question  experimentally,  but  the 
views  of  Clausius  appear  to  be  most  in  accordance  with  the 
dynamic  theory  of  heat. 


HEAT.  45 

116.  Elastic  Force  of  Vapors. — The  elastic  force  of  satu- 
!     rated  vapors  may  be  illustrated  experimentally  by  taking  several 

barometer-tubes*  filling  them  with  mercury,  and  inserting  themV 
in  a  trough  of  mercury.  The  surface  of  the  mercury  in  each 
tube  will  drop  about  six  inches,  leaving  a  vacuous  space  at  the 
top  of  the  tube.  If  now  a  small  quantity  of  liquid  water  be 
passed  up  into  this  vacuous  space  in  one  tube,  alcohol  into  an- 
other, and  ether  into  another,  the  quantity  of  liquid  being  more 
than  can  be  evaporated  in  each  space  at  ordinary  temperatures, 
it  will  be  found  that  a  portion  of  each  liquid  will  be  instantly 
evaporated,  and  the  mercurial  column  will  be  depressed  in  each 
tube,  but  by  different  amounts.  If  each  tube  be  now  heated  by 
surrounding  it  with  warm  water,  the  elastic  force  of  each  vapor 
will  be  increased,  the  mercury  will  descend  in  the  tubes,  and 
will  finally  press  the  mercurial  column  down  to  the  level  of  the 
reservoir.  At  this  point  it  is  evident  that  the  elastic  force  of 
each  vapor  is  equal  to  that  of  the  atmosphere,  or  1  atmosphere. 
But  the  temperature  of  the  liquid  and  vapor  in  each  tube  will 
be  different  from  that  in  the  others. 

The  temperature  of  the  watery  vapor  will  be  found  to  be 
212°  Fahr.,  the  temperature  of  the  alcohol  173°,  and  the  tem- 
perature of  the  ether  95°  Fahr.  These  are  the  temperatures  at 
which  the  elastic  forces  of  these  vapors  are  equal,  respectively, 
to  one  atmosphere.  At  these  temperatures  the  liquids  will  boil, 
under  the  atmospheric  pressure. 

If  the  temperatures  be  reduced  below  these  points,  the 
pressure  remaining  the  same,  a  portion  of  the  vapor  in  each 
tube  will  be  liquefied  ;  and,  the  temperatures  remaining  the 
same,  if  the  pressure  be  increased  above  one  atmosphere,  a 
portion  of  each  vapor  will  become  liquefied.  The  tension  or 
elastic  force  of  one  atmosphere  is  thus  the  maximum  tension 
which  the  saturated  vapors  can  bear  at  the  temperatures  given 
above. 

If  the  three  tubes  could  be  enclosed  in  a  chamber  in  which, 
by  compression  of  the  air,  different  pressures  can  be  obtained 
higher  than  one  atmosphere,  it  would  be  found  that,  for  each  of 
the  substances  named,  the  temperatures  at  which  the  mercury 
will  be^  forced  down  to  the  level  of  the  reservoir  under  each 
additional  atmosphere  of  pressure,  will  be  increased. 

117.  The  following  table  gives  the  results  of  experiments  by 
Regnault  for  the  liquids  named : 


46 


HEAT. 


XI. 


Pressure  in  Atmospheres. 

Temperature  of  the  saturated 
vapor  in  deg.  Fahr. 

I* 

1             

Water. 

212° 
248° 
272° 
291° 
306° 
318.5 
329.5 
339° 
348° 
357° 

Alcohol. 

173° 

206° 

227° 

257° 
269° 
280° 
288° 
297° 
305° 

Ether. 

95° 
133° 

157° 
176° 

192° 
206° 

218° 
228° 
238° 

247° 

2  

3  

4  

5  

6  

7  
8  

9               

10  

The  numbers  of  this  table  are  taken  from  Zeuner's  work,  "  de 
la  Chaleur,"  French  edition ;  the  temperatures  being  convert- 
ed from  C.  to  F. 

118.  The  elastic  force  of  saturated  vapors  is  thus  independent 
of  the  volume  and  proportion  of  liquid  mixed  with  the  vapor, 
and  depends  only  on  the  temperature. 

119.  It  has  been  found  impossible  to  determine,  theoretically, 
the  relation  which  the  temperatures  bear  to  the  pressures,  and 
reliance  is  placed  mainly  on  the  celebrated  experiments  of  Re- 
gnault.     On  account  of  the  universal  employment  of  steam  in 
practical  applications,  the  importance  of  the  results  can  hardly 
be  sufficiently  estimated.     Regnault's  tables,  in  fact,  constitute 
the  basis  of  all  theoretical  applications  of  heat  through  the  me- 
dium of  steam ;  giving  as  they  do,  in  exact  figures,  the  elastic 
force  of  saturated  steam  for  all  usual  temperatures. 

These  tables  show  that  110  simple  relation  exists  between  the 
maximum  tension  and  the  temperature.  Different  empirical 
formulas  have  been  proposed,  however,  to  express  this  relation 
with  certain  degrees  of  approximation. 

Some  of  these  are  convenient  for  use  when  the  tables  of 
Regnault  are  not  at  hand ;  while  others  are  too  complicated  for 
ready  use. 

Among  the  simple  formulas,  the  following  are  mentioned  in 
the  admirable  work  of  Morin  and  Tresca,  "  des  Machines  a 
Yapeur.  Vol.  I.  Production  de  la  Vapeur." 


HEAT.  47 

N  representing  the  pressure  in  atmospheres,  and  t  the  tempe- 
rature in  degrees  Centigrade,  the  formulas  are  as  follows  : 

Formula  of  Dalton. 


Formula  of  Tredgold. 

i    6 


t=lT5 

Formula  of  Roche. 

locr    TST 

t=100  + 


0.01494  —  0.00277  log.  N 

t-100 

H=1.08B   1+0-002727  (t-100) 


Formula  of  Coriolis. 

5.855   /  — 

_2.878      VN  ~: 
t — 


0.01878 

1  +  0.01878- 5t855 
~^878" 


Formula  of  Arago  and  Dulong. 

5 


Of  these  formulas  that  of  Tredgold  appears  the  most  simple 
and  exact. 

The  formula  of  Kegnault  is  the  only  one  which  is  perfectly 
exact.  It  is  not  given  here,  being  too  complicated  for  general 
use,  but  may  be  referred  to  in  the  work  above  cited. 

The  following  table  of  comparisons,  taken  from  Morin  and 
Tresca,  shows  the  degrees  of  exactness  of  the  different  formulas  : 

J.    JU)  \>V-C  ^Ls-    OLXW  ^Arcjxy  *.    "3-1  o-^ 

U- 


HEAT. 


TABLE  XII. 

Comparison  between  tJie  values  of  the  Temperatures  according  to  the  different 

Formulas. 


Pressures 
in  Atmos- 
pheres. 

Temperatures 
observed  by 
Kegnault. 

Formula  of 
Dulton. 

Formula  of 
Tredgold. 

Formula  of 
Koche. 

Formula  of 
Coriolis. 

Formula  of 
Arago  and 
Dulong. 

1 

100. 

100. 

100.0 

100  0 

100.0 

100.0 

2 

120.6 

122.7 

121.4 

121.3 

121.2 

120.8 

5 

152.2 

152.9 

153.8 

153.6 

153.7 

153.1 

10 

180.3 

175.8 

181.9 

182.6 

182.8 

181.8 

15 

198.8 

189.1 

200.9 

200.4 

200.9 

200.5 

20 

213.0 

198.6 

213.3 

214.2 

215.5 

214.6 

25 

224.7 

205.9 

224  3 

330.4 

226.3 

226.3 

120.  Regnault's  Experiments. — The  following  table  of 
temperatures  and  pressures  has  been  prepared  from  the  cor- 
responding tables  given  by  Morin  and  Tresca  as  the  results  of 
Regnault's  experiments  on  the  pressures  and  temperatures  of 
saturated  steam ;  the  necessary  transformations  and  interpola- 
tions having  been  made  to  give  the  temperatures  in  degrees 
Fahr.,  and  the  pressures  in  pounds  per  square  inch : 

TABLE   XIII. 

Table  of  pressures  of  the  saturated  vapor  of  Water,  from  32°  to  446°  Fahrenheit, 
from  the  experiments  of  Regnault. 


Temp. 
Fahr. 

Pressures 
in 
Atmospheres. 

Pressures 
in  Ibs.  per 
sq.  inch. 

Differ- 
ences. 

Temp. 
Fahr. 

Pressures 
in 
Atmospheres. 

Pressures 
in  Ibs.  per 
sq.  inch. 

Differ- 
ences. 

32 

0.006 

0.09 

0.00 

49 

0.011 

0.17 

0.01 

33 

0.006 

0.09 

0.00 

50 

0.012 

0.18 

0.00 

34 

0.006 

0.09 

0.01 

51 

0.012 

0.18 

0.01 

35 

0.007 

0.10 

0.00 

52 

0.013 

0.19 

0.01 

36 

0.007 

0.10 

0.01 

53 

0.013 

0.20 

0.01 

37 

0.007 

0.11 

0.01 

54 

0.014 

0.21 

0.00 

38 

0.008 

0.12 

0.00 

55 

0.014 

0.21 

0.01 

39 

0.008 

0.12 

0.01 

56 

0.015 

0.22 

0.02 

40 

0.009 

0.13 

0.00 

57 

0.016 

0.24 

0.00 

41 

0.009 

0.13 

0.01 

58 

0.016 

0.24 

0.01 

42 

0.009 

0.14 

0.00 

59 

0.017 

0.25 

0.01 

43 

0.009 

0.14 

0.01 

60 

0.018 

0.26 

0.00 

44 

0.010 

0.15 

0.00 

61 

0.018 

0.26 

0.00 

45 

0.010 

0.15 

0.01 

62 

0.018 

0.26 

0.02 

46 

0.011 

0.16 

0.00 

63 

0.019 

0.28 

0.01 

47 

0.011 

0.16 

0.01 

64 

0.020 

0.29 

0.00 

48 

0.011 

0.17 

0.00 

65 

0.020 

0.29 

0.02 

HEAT. 


TABLE 


.—  Continued. 


Temp. 

Pressures 
in 

Pressures 
in  Ibs.  per 

Differ- 

Temp. 

Pressures 
in 

Pressures 
in  Ibs.  per 

Differ- 

Fahr. 

Atmospheres. 

sq.  inch. 

Fahr. 

Atmospheres. 

sq.  inch. 

66 

0.021 

0.31 

0.01 

117 

0.105 

1.54 

0.03 

67 

0.022 

0.32 

0.02 

118 

0.1Q7 

1.57 

0.08 

68 

0.023 

0.34 

0.00 

119 

0.112 

1.65 

0.03 

69 

0.023 

0.34 

0.01 

120 

0.114 

1.68 

0.04 

70 

0.024 

0.35 

0.00 

131 

0.117 

1.72 

0.06 

71 

0.024 

0.35 

0.02 

122 

0.121 

1.78 

0.04 

72 

0.025 

0.37 

0.01 

123 

0.124 

1.82 

0.05 

73 

0.026 

038 

0.02 

124 

0.127 

1.87 

0.04 

74 

0.027 

0.40 

0.01 

125 

0.130 

1.91 

0.09 

75 

0.028 

0.41 

0.02 

126 

0.136 

2.00 

0.04 

76 

0.029 

0.43 

0.03 

127 

0.139 

2.04 

0.05 

77 

0.031 

0.46 

0.00 

128 

0.142 

2.09 

0.06 

78 

0.031 

0.46 

0.01 

129 

0.146 

2.15 

0.05 

79 

0.032 

0.47 

0.00 

130 

0.150 

2.20 

0.06 

80 

0.032 

0.47 

0.02 

131 

0.154 

2.26 

0.06 

81 

0.033 

0.49 

0.01 

132 

0.158 

2.32 

0.06 

82 

0.034 

0.50 

0.03 

133 

0.162 

2.38 

0.06 

83 

0.036 

0.53 

0.01 

134 

0.166 

2.44 

0.09 

84 

0.037 

0.54 

0.03 

135 

0.172 

2.53 

0.04 

85 

0.039 

0.57 

0.03 

136 

0.175 

2.57 

0.09 

86 

0.041 

0.60 

0.02 

137 

0.181 

2.66 

0.03 

87 

0.042 

0.62 

0.01 

138 

0.183 

2.69 

0.12 

88 

0.043 

0.63 

0.02 

139 

0.191 

2.81 

0.07 

89 

0.044 

0.65 

0.03 

140 

0.196 

2.88 

0.06 

90 

0.046 

0.68 

0.03 

141 

0.200 

2.94 

0.07 

91 

0.048 

0.71 

0.01 

142 

0.205 

3.01 

0.08 

92 

0.049 

0.72 

0.02 

143 

0.210 

3.09 

0.10 

93 

0-050 

0.74 

0.02 

144 

0.217 

3.19 

0.04 

94 

0.052 

0.76 

0.05 

145 

0.220 

3.23 

0.09 

95 

0.055 

0.81 

0.03 

146 

0.226 

3.32 

0.08 

96 

0.057 

0.84 

0.01 

147 

0.231 

3.40 

0.10 

97 

0.058 

0.85 

0.05 

|     148 

0.238 

3.50 

0.10 

98 

0.061 

0.90 

0.00 

149 

0.245 

3.60 

0.09 

99 

0.061 

0.90 

0.03 

150 

0.251 

3.69 

0.12 

100 

0.063 

0.93 

0.04 

151 

0.259 

3.81 

0.09 

101 

0.066 

0.97 

0.01 

152 

0.265 

3.90 

0.08 

102 

0.067 

0.98 

0.03 

153 

0.271 

3.98 

0.11 

103 

0.069 

1.01 

0.05 

154 

0.278 

4.09 

0.10 

104 

0.072 

1.06 

0.03 

155 

0.285 

4.19 

0.06 

105 

0.074 

1.09 

0.06 

156 

0.289 

4.25 

0.16 

106 

0.078 

1.15 

0.01 

157 

0.300 

4.41 

0.09 

407 

0.079 

1.16 

0.02 

158 

0.306 

4.50 

0.03 

108 

0.080 

1.18 

0.04 

159 

0.308 

4.53 

0.14 

109 

0.083 

1.22 

0.04 

160 

0.318 

4.67 

0.11 

110 

0.086 

1.26 

0.03 

161 

0.325 

4.78 

0.19 

111 

0.088 

1.29 

0.05 

162 

0.338 

4.97 

0.10 

112 

0.091 

1.34 

0.03 

163 

0.345 

5.07 

0.12 

113 

0.093 

1.37 

0.03 

164 

0.353 

5.19 

0.12 

114 

0.095 

1.40 

0.07 

165 

0.361 

5.31 

0.14 

115 

0.100 

1.47 

0.03 

166 

0.371 

5.45 

0.12 

116 

0.102 

1.50 

0.04 

167 

0.879 

5.57 

1.02 

50 


HEAT. 
TABLE  -KIIL.— Continued. 


Temp, 
degrees 
Fahr. 

Pressure 
in 
Atmospheres. 

Pressure 
in  Ibs.  per 
sq.  inch. 

Differ- 
ences. 

Temp, 
degrees 
Fahr. 

Pressure 
in 

Atmospheres. 

Pressure 
in  Ibs.  per 
sq.  inch. 

Differ- 
ences. 

168 

0.387 

5.69 

0.13 

219 

1.147 

16.86 

0.32 

169 

0.396 

5.82 

0.13 

220 

1.169 

17.18 

0.33 

170 

0.405 

5.95 

0.15 

221 

1.191 

17.51 

0.35 

171 

0.415 

6.10 

0.15 

222 

1.215 

17.86 

0.34 

172 

0.425     |       6.25 

0.16 

223 

1.238 

18.20 

0.34 

173 

0.436 

6.41 

0.13 

224 

1.261 

18.54 

0.35 

174 

0.445 

6.54 

0.15 

225 

1.285 

18.89 

0.35 

175 

0.455 

6.69 

0.16 

226 

1.309 

19.24 

0.37 

176 

0.466 

6.85 

0.15 

227 

1.334 

19.61 

0.37 

177 

0.476 

7.00 

0.15 

228 

1.359 

19.98 

0.38 

178 

0.488 

7.15 

0.21 

229 

1.385 

20.36 

'    0.44 

179 

0.501 

7.36 

0.18 

230 

1.415 

20.80 

0.40 

180 

0.513 

7.54 

0.12 

231 

1.442 

21.20 

0.39 

181 

0.521 

7.66 

0.15 

232 

1.469 

21.59 

0.42 

182 

0.531 

7.81 

0.17 

233 

1.497 

22.01 

0.41 

183 

0.543 

7.98 

0.19 

234 

1.525 

22.42 

0.41 

184 

0.556 

8.17 

0.19 

235 

1.553 

22.83 

0.43 

185 

0.569 

8.36 

0.18 

236 

1.582 

23.26 

0.44 

186 

0.581 

8.54 

0.18 

237 

1.612 

23.70 

0.42 

187 

0.593 

8.72 

0.17 

238 

1.641 

24.12 

0.43 

188 

0.605 

8.89 

0.19 

239 

1.670 

24.55 

0.44 

189 

0.618 

9.08 

0.21 

240 

1.700 

24.99 

0.45 

190 

0.632 

9.29 

0.21 

241 

1.731 

25.45 

0.45 

191 

0.646 

9.50 

0.22 

242 

1.762 

25.90 

0.47 

192 

0.661 

9.72 

0.22 

243 

1.794 

26.37 

0.47 

193 

0.676 

9.94 

0.22 

244 

1.826 

26.84 

0.49 

194 

0.691 

10.16 

0.20 

245 

1.859 

27.33 

0.50 

195 

0.705 

10.36 

0.21 

246 

1.893 

27.83 

0.51 

196 

0.719 

10.57 

0.22 

247 

1.928 

28.34 

0.50 

197 

0.734 

10.79 

0.22 

248 

1.962 

28.84 

0.52 

198 

0.749 

11.01 

0.22 

249 

1.997 

29.36 

0.51 

199 

0.764 

11.23 

0.22 

250 

2.032 

29.87 

0.53 

200 

0.770 

11.45 

0.12 

251 

2.068 

30.40 

0.53 

201 

0.787 

11.57 

0.25 

252 

2.104 

30.93 

0.54 

202 

0.804 

11.82 

0.43 

253 

2.141 

31.47 

0.56 

203 

0.833 

12.25 

0.25 

254 

2.179 

32.03 

0.57 

204 

0.850 

12.50 

0.24 

255 

2.217 

32.60 

0.56 

205 

0.867 

12.74 

0.27 

256 

2.256 

33.16 

0.56 

206 

•    0.885 

13.01 

0.28 

257 

2.294 

33.72 

0.59 

207 

0.904 

13.29 

0.28 

258 

2.334 

34.31 

0.59 

208 

0.923 

13.57 

0.28 

259 

2.374 

34.90 

0.60 

209 

0.942 

13.85 

0.28 

260 

2.415 

35.50 

0.60 

210 

0.961 

14.13 

0.29 

261 

2.456 

36.10 

0.62 

211 
212 

0.981 
1.000 

14.42 

14.  #7 

0.28 
0.30 

262 
263 

2.498 
2.541 

36.72 
37.35 

0.63 
0.63 

213 

1.020 

15.00 

0.29 

I     264 

2.584 

37.98 

0.64 

214 

1.040 

15.29 

0.31 

265 

2.627 

38.62 

0.64 

215 

1.061 

15.60 

0.32 

266 

2.671 

39.26 

0.67 

216 

1.083 

15.92 

0.31 

267 

2.716 

39.93 

0.66 

217 

1.104 

16.23 

0.31 

268 

2.761 

40.59 

0.67 

218 

1.125 

16.54 

0.32 

269 

2.807 

41.26 

0.69 

HEAT. 
TABLE  XIII.— Continued. 


51 


Temp, 
degrees 
Fahr. 

Pressure 
in 

Atmospheres. 

Pressure 
in  Ibs.  per 
sq.  inch. 

Differ- 
ences. 

T~mp. 
degrees 
Fahr. 

Pressure 
in 
Atmospheres. 

Pressure 
in  Ibs.  per 
sq.  inch. 

Differ- 
ences. 

270 

2.854 

41.95 

0.69 

321 

6.208 

91.26 

1.29 

271 

2.901 

42.64 

0.71 

322 

6.296 

92.55 

1.31 

272 

2.949  • 

43.35 

0.71 

323 

6.385 

93.86 

1.32 

273 

2.997 

44.06 

0.72 

324 

6.475 

95.18 

1.34 

274 

3.046 

44.78 

0.75 

325 

6.566 

96.52 

1.35 

275 

3.097 

45.53 

0.73 

326 

6.658 

97.87 

1.37 

276 

3.147 

46.26 

0.75 

327 

6.751 

99.24 

1.40 

277 

3.198 

47.01 

0.77 

328 

6.846 

100.64 

1.45 

278 

3.250 

47.78 

0.77 

329 

6.945 

102.09 

1.44 

279 

3.303 

48.55 

0.80 

330 

7.043 

103.53 

1.44 

280 

3.357 

49.35 

0.79 

331 

7.141 

104.97 

1.44 

281 

3.411  . 

50.14 

0.81 

332 

7.239 

106.41 

1.46 

282 

3.466 

50.95 

0.81 

333 

7.338 

107.87 

1.45 

283 

3.521 

51.76 

0.81 

334 

7.437 

109.32 

1.46 

284 

3.576 

52.57 

0.82 

335 

7.536 

110.78 

.50 

285 

3.632 

53.39 

0.84 

336 

7.638 

112.28 

.51 

286 

3.689 

54.23 

0.85 

337 

7.741 

113.79 

.55 

287 

3.747 

55.08 

0.87 

338 

7.846 

115.34 

.55 

288 

3.806 

55.95 

0.88 

339 

7.952 

116.89 

.59 

289 

3.866 

56.83    , 

0.88 

340 

8.060 

118.48 

.60 

290 

3.926 

57.71 

0.90 

341 

8.169 

120.08 

1.62 

291 

3.987 

58.61 

0.91 

342 

8.279 

121.70 

1.62 

292 

4.049 

59.52 

0.93 

343 

8.389 

123.32 

1.63 

293 

4.112 

60.45 

0.92 

344 

8.500 

124.95 

1.65 

294 

4.175 

61.37 

0.94 

345 

8.612 

126.60 

1.64 

295 

4.239 

62.31 

0.96 

346 

8.724 

128.24 

1.68 

296 

4.304 

63.27 

0.97 

347 

8.838 

129.92 

1.69 

297 

4.370 

64.24 

0.98 

348 

8.953 

131.61 

1.72 

298 

4.437 

65.22 

1.00 

349 

9.070 

133.33 

1.75 

299 

4.505 

66.22 

1.02 

350 

9.189 

135.08 

1.78 

300 

4.574 

67.24 

1.01 

351 

9.310 

136.86 

1.81 

301 

4.643 

68.25 

1.02 

352 

9.433 

138.67 

1.80 

302 

4.712 

69.27 

1.03 

353 

9.556 

140.47 

1.83 

303 

4.782 

70.30 

1.04 

354 

9.680 

142.30 

1.82 

304 

4.853 

71.34 

1.06 

355 

9.804 

144.12 

1.84 

305 

4.925 

72.40 

1.07 

356 

9.929 

145.96 

1.85 

306 

4.998 

73.47 

1.09 

357 

10.055 

147.81 

1.87 

307 

5.072 

74.56 

1.10 

358 

10.182 

149.68 

1.89 

308 

5.147 

75.66 

1.12 

359 

10.311 

151.57 

1.93 

309 

5.223 

76.78 

1.13 

360 

10.442 

153.50 

1.95 

310 

5.300 

77.91 

1.16 

361 

10.575 

155.45 

1.99 

311 

5.379 

79.07 

1.16 

362 

10.710 

157.44 

2.01 

312 

5.458 

80.23 

1.18 

363 

10.847 

159.45 

2.03 

313 

5.538 

81.41 

1.19 

364 

10.985 

161.48 

2.03 

314 

5.619 

82.60 

1.20 

365 

11.123 

163.51 

2.04 

315 

5.701 

83.80 

1.22 

366 

11.262 

165.55 

2.04 

316 

5.784 

85.02 

1.22 

367 

11.401 

167.59 

2.08 

317 

5.867 

86.24 

1.24 

368 

11.542 

169.67 

2.08 

318 

5.951 

87.48 

1.23 

369 

11.684 

171.75 

2.14 

319 

6.035 

88.71 

1.27 

370 

11.829 

173.89 

2.16 

320 

6.121 

89.98 

1.28 

371 

11.976 

176.05 

2.19 

52 


HEAT. 
TABLE  XIII.— Continued. 


Temp, 
degrees 
Fahr. 

Pressure 
in 
Atmospheres. 

Pressure 
in  Ibs.  per 
sq.  inch. 

Differ- 
ences. 

Temp, 
degrees 
Fahr. 

Pressure 
in 
Atmospheres. 

Pressure 
in  Ibs.  per 
sq.  inch. 

Differ- 
ences, 

372 

12.125 

178.24 

2.19 

410 

18.848 

277.07 

3.16 

373 

12.274 

180.43 

2.22 

411 

19.063 

280.23 

3.19 

374 

12.425 

182.65 

2.22 

412 

19.280 

283.42 

3.19 

375 

12.576 

184.87 

2.23 

413 

19.497 

286.61 

3.19 

376 

12.728 

187.10 

2.25 

414 

19.714 

289.80 

3.19 

377 

12.881 

189.35 

2.26 

415 

19.931 

292.99 

3.19 

378 

13.035 

191.61 

2.28 

416 

20.148 

296.18 

3.19 

379 

13.190 

193.89 

2.31 

417 

20.365 

299.37 

3.19 

380 

13.347 

196.20 

2.35 

418 

20.582 

302.56 

3.07 

381 

13.507 

198.55 

2.40 

419 

20.791 

305.63 

3.38 

382 

13.670 

200.95 

2.44 

420 

21.021 

309.01 

3.38 

383 

13.836 

203.39 

2.45 

421 

21.251 

312.39 

3.38, 

384 

14.003 

205.84 

2.47 

422 

21.481 

315.77 

3.38 

385 

14.171 

208.31 

2.49 

423 

21.711 

319.15 

3.44 

386 

14.340 

210.80 

2.50 

424 

21.945 

322.59 

3.32 

387 

14.510 

213.30 

2.51 

425 

22.171 

325.91 

3.38 

388 

14.681 

215.81 

2.54 

426 

22.401 

329.29 

3.39 

389 

14.854 

218.35 

2.58 

427 

22.631 

332.68 

3.83 

390 

15.029 

220.93 

2.60 

428 

22.892 

336.51 

3.53 

391 

15.206 

223.53 

2.56 

429 

23.132 

340.04 

3.53 

392 

15.380 

226.09 

1.13 

430 

23.372 

343.57 

3.53 

393 

15.457 

227.22 

2.64 

431 

23.612 

347.10 

3.52 

394 

15.637 

229.86 

2.69 

432 

23.852 

350.62 

3.68 

395 

15.820 

232.55 

2.65 

433 

24.102 

354.30 

3.67 

396 

16.000 

235.20 

2.79 

434 

24.352 

357.97 

3.68 

397 

16.190 

237.99 

2.87 

435 

24.602 

361.65 

3.67 

398 

16.385 

240.86 

2.90 

436 

24.852 

365.32 

3.91 

399 

16.582 

243.76 

2.94 

437 

25.118 

369.23 

3.83 

400 

16.782 

246.70 

3.04 

438 

25.378 

373.06 

3.82 

401 

16.989 

249.74 

3.47 

439 

25.638 

376.88 

3.82 

402 

17.225 

253.21 

3.03 

440 

25.898 

380.70 

3.90 

403 

17.431 

256.24 

3.04 

441 

26.163 

384.60 

3.97 

404 

17.638 

259.28 

3.07 

442 

26.433 

388.57 

4.11 

405 

17.847 

262.35 

3.04 

443 

26.713 

392.68 

4.12 

406 

18.054 

265.39 

3.05 

444 

26.993 

396.80 

4.11 

407 

18.261 

268.44 

3.04 

445 

27.273 

400.91 

4.12 

408 

18.468 

271.48 

3.04 

446 

27.553 

405.03 

409 

18.675 

274.52 

2.55 

121.  The  most  remarkable  feature  in  these  results  is  the  change 
in  the  rate  of  increase  of  pressure  for  one  degree  of  tempera- 
ture. At  abont  212°,  the  rate  of  increase  for  one  degree  rise  of 
temperature  is  about  0.3  of  a  pound ;  at  250°,  it  is  0.5  of  a 
pound  ;  at  300°,  about  1  pound  ;  at  350°,  1.8  pounds ;  at  400°, 
about  3  pounds ;  and  at  446°,  4.1  pounds. 

The  following  diagram  exhibits  this  law  to  the  eye  at  a 
glance.  It  is  a  graphical  representation,  on  a  small  scale,  of 


HEAT. 


53 


the  relation  between  the  temperatures  and  pressures  from  Ke- 
gnault's  experiments. 


FIG.  1. 


I  B  R  A  R 
1  -N'JVEHfsrr 
t  CALIFORNIA 


14.7 


446° 


TEMPERATURES. 

122.  It  is  often  convenient  to  refer  to  a  corresponding  table  in 
which  the  pressures  are  given  in  the  first  column,  increasing 
by  one  pound — the  corresponding  temperatures  Fahr.  being 
introduced  in  the  next  column. 

Such  a  table  may  be  found  in  many  English  works,  and  that 
which  is  found  in  Fairbairn's  "  Mills  and  Mill-work "  is  here 
introduced. 

The  rate  of  decrease  of  temperature  with  the  pressure  is 
shown  in  the  column  of  differences— the  third  column. 

At  1  Ib.  pressure  (102°)  it  requires  a  rise  of  temperature  of 
24°  to  increase  the  pressure  to  2  Ibs. ;  at  14.7  Ibs.  (1  atmos- 
phere) it  requires  an  increase  of  temperature  of  3.5°  only,  for 
an  increase  1  Ib.  pressure  ;  at  30  Ibs.  about  2°  ;  at  TO  Ibs.  1°  ; 
at  100  Ibs.  0.7° ;  at  250  Ibs.  0.4°  Fahr. 


HEAT. 


TABLE  XIV. 

"  Of  the  pressure  and  corresponding  temperature  of  saturated  steam,  obtained 
from  the  tables  of  M.  Regnault,  by  interpolation  and  reduction  to  English 
measures."  (FAIRBAIRN.) 


Pressure  in  Ibs. 
per  sq.  inch. 

Temp,  in  de- 
grees Fahr. 

Hise  of  temp,  for 
1  Ib.  pres. 

Pressure  in  Ibs. 
per  sq.  men. 

Temp,  in  de- 
grees Fahr. 

1 
t| 

P 

PH 

Pressure  in  Ibs. 
per  sq.  inch. 

Temp,  in  de 
grees  Fahr. 

Ripe  of  temp,  for 
1  Ib.  pres. 

1 

102. 

24.3 

32 

253.9 

1.8 

75 

307.4 

0.9 

2 

126.3 

33 

255.7 

1.8 

80 

311.8 

0.9 

3 

141.6 

15.4 

34 

257.5 

1.7 

85 

316.0 

0.8 

4 

153.1 

11.5 

35 

259.2 

1.7 

90 

320.0 

0.8 

5 

162.3 

9.3 

36 

260.8 

1.6 

95 

323.9 

0.7 

6 

170.1 

7.8 

37 

262.4 

1.6 

100 

327.6 

0.7 

7 

176.9 

6.8 

38 

264.0 

1.5 

105 

331.1 

0.7 

8 

182.9 

6.0 

39 

2(55.6 

1.5 

110 

334.5 

0.7 

9 

188.3 

5.4 

40 

267.1 

1.5 

115 

337.8 

0.6 

10 

193.2 

4.9 

41 

268.6 

1.5 

120 

341.0 

0.6 

11. 

197.8 

4.5 

42 

270.1 

1.4 

125 

344.1 

0.6 

12 

202.0 

4.2 

43 

271.5 

1.4 

130 

347.1 

0.6 

13 

205.9 

3.9 

44 

272.9 

1.4 

135 

350.0 

0.6 

14 

209.6 

3.7 

45 

274.3 

1.4 

140 

352.8 

0.6 

14.7 

212. 

46 

275.7 

1.3 

145 

355.6 

0.6 

15 

213. 

3.5 

47 

277.0 

1.3 

150 

358.3 

0.5 

16 

216.3 

3.3 

48 

278.3 

1.3 

160 

363.4 

0.5 

17 

219.4 

3.1 

49 

279.6 

1.3 

170 

368.2 

05 

18 

222.4 

3.0 

50 

280.9 

1.3 

180 

372.9 

0.5 

19 

225.2 

2.8 

51 

282.6 

1.2 

190 

377.5 

0.4 

20 

227.9 

2.7 

52 

283.3 

1.2 

200 

381.8 

0.4 

21 

230.5 

2.6 

53 

284.5 

1.2 

210 

386.0 

0.4 

22 

233.1 

2.5 

54 

285.7 

1.2 

220 

389.9 

0.4 

23 

235.5 

2.3 

55 

286.9 

1.2 

230 

393.8 

0.4 

24 

237.8 

2.3 

56 

288.1 

1.1 

240 

397.5 

0.4 

25 

240.0 

2.8 

57 

289.2 

1.1 

250 

401.1 

0.3 

26 

242.2 

2.2 

58 

290.3 

1.1 

260 

404.5 

0.3 

27 

244.3 

2.1 

59 

291.4 

1.1 

270 

407.9 

0.3 

28 

246.3 

2.0 

60 

292.5 

1.1 

280 

411.2 

0.3 

29 

248.3 

2. 

65 

297.8 

1. 

290 

414.4 

0.3 

30 

250.2 

1.9 

70 

302.7 

300 

417.5 

31 

252.1 

1.9 

32 

253.9 

1.9 

HEAT.  55 


LATENT  HEAT. 

123.  The  effects  which  follow  the  transferring  of  heat  to  a 
body,  solid,  liquid,  or  gaseous,  have  been  described  by  employ- 
ing the  simple  algebraic  expression, 


772 

The  quantity  A  represents  a  change  which  is  exhibited  by  a 
change  of  sensible  heat,  or  change  of  temperature.  That  part  of 
the  whole  heat  transferred  which  produces  the  work  B  and  the 
work  c  is  expended  in  producing  a  change  in  the  relative  posi- 
tions of  the  particles,  and  in  external  work  ;  and  disappears  as 
sensible  heat,  i.e.,,  it  is  not  afterwards  contained  in  the  body,  or 
exhibited  in  the  body,  as  heat.  These  quantities  of  heat  re- 

B  c 

presented  by  ==o  and  ^=^  become  latent. 

The  term  latent  heat  is  a  technical  expression,  designating  a 
quantity  of  heat  which  has  apparently  disappeared,  but  which 
really  has  been  employed  in  producing  changes  in  the  body,  in 
the  form  of  work,  other  than  the  change  of  velocity  of  mo- 
lecular motion,  or  change  of  temperature.  By  reversing  the 
process  by  which  heat  is  thus  made  to  disappear,  this  latent 
heat  may  be  reproduced. 

In  thus  separating  the  effects  of  a  given  quantity  of  heat  Q 
into  the  parts  A,  B,  and  c,  the  true  theories  of  the  coefficient  of 
expansion,  specific  heat,  and  latent  heat  become  susceptible  of 
rational  explanation.  Of  these  quantities,  A  and  c,  for  any 
change  of  heat  in  a  body,  can  usually  be  numerically  estimated  ; 
the  change  A  being  directly  proportional  to  T,  the  change  of  ab- 
solute temperature,  and  the  change  c  being  the  product  of  the 
external  pressure  multiplied  by  the  change  of  volume  of  the 
body.  The  quantity  B,  however,  cannot  thus  be  separately 
calculated,  because  there  is  not,  in  the  present  state  of  science, 
sufficient  knowledge  of  molecular  attractions  to  compute  directly 
the  work  performed  in  overcoming  these  attractions  for  a  given 
change  of  volume.  This  is  not  important,  however,  because 
this  quantity  may  be  found  from  the  expression, 

A  +   B   +   0 

Q= 


772 


56  HEAT. 

when  Q,  A,  and  c  are  known.  And,  moreover,  it  happens  in  the 
action  of  bodies  under  the  influence  of  heat,  that  in  the  solid 
and  liquid  forms,  for  nearly  all  bodies,  the  quantity  c  is  so 
small  for  the  extreme  range  of  temperature  belonging  to  those 
states,  that  for  technical  purposes  it  may  be  neglected  ;  while, 
on  the  other  hand,  after  the  body  has  passed  to  the  state  of 
vapor  or  gas,  the  quantity  o  becomes  large,  and  the  quantity 
B,  so  small  that  it  may  be  neglected. 

The  latent  heat  which,  in  the  most  general  case,  is  repre- 

sented by  -  —  (B  -f  c)  becomes  for  solids  and  liquids,  practically, 

rT2 

—  —  B  and  for  gases,  especially  perfect  gases,  —  c.     In  other 

772  772 

words,  in  the  case  of  solids  and  liquids,  for  all  practical  pur- 
poses, the  effect  of  the  exterior  pressure  may  be  neglected, 
and  in  the  case  of  perfect  gases  and  vapors,  the  internal  work 
may  be  regarded  as  simply  confined  to  the  change  of  molecular 
vibration. 

The  specific  heat  of  a  solid  or  liquid  may  be  regarded,  there- 
fore, as  equivalent  to 


-       being  the  quantity  of  heat,  in  units  of  heat,  which  remain  in 


1  Ib.  of  the  substance  after  an  increase  of  temperature  of  1° 
Fahr.,  and  -—  -  being  the  latent  heat  of  expansion  of  1  Ib.  of  the 

substance  for  1°  rise  of  temperature. 

Practically,  this  quantity,  or  the  latent  heat  of  expansion,  is 
included  in  the  specific  heat,  for  ordinary  solids  and  liquids, 
the  quantities  a  and  b  not  being  separated.  The  amount  of 
heat  necessary  to  raise  one  pound  of  a  solid  any  number  of  de- 
grees in  temperature  is  thus  c,  the  specific  heat,  multiplied  by  t, 
the  number  of  degrees,  c  being  the  mean  specific  heat  of  the 
solid  for  the  given  range  of  temperature. 

A  remarkable  change  occurs,  however,  in  the  relative  values 
of  the  quantities  A,  B,  and  c  when  a  body  changes  its  state  from 
solid  to  liquid,  or  from  liquid  to  gaseous. 

At  the  melting-point,  the  quantity  A  vanishes  suddenly  or 
gradually,  and  the  addition  of  heat,  after  that,  does  not  raise 
the  temperature  of  the  residual  mass  of  solid,  or  that  part  which 
has  become  liquid,  each  additional  unit  of  heat  being  expended 


HEAT.  57 

in  the  work  designated  by  B  -f  c  ;  B  being  the  greater,  and  c 
being  usually  very  small,  and  sometimes  negative. 

124.  Latent   Heat   of  Fusion.—  This   quantity  -EJT  °for 

each  Ib.  of  the  substance  melted  is  called  the  latent  heat  of 
fusion,  and  its  value  in  units  of  heat  for  various  substances  has 
already  been  given,  page  21. 

After  the  body  has  all  passed  to  the  liquid  state,  if  heat  be 
still  applied,  the  quantity  A  reappears  (the  substance  is  further 
heated  and  the  temperature  rises),  and  from  the  melting-point 
to  the  boiling-point  the  quantity  of  heat  necessary  to  raise  the 
temperature  of  the  body  1°  Fahr.  is  again  composed  of  the  three 
terms  A,  B,  and  c  ;  o  being,  as  in  the  solid  state,  very  small, 
since  the  expansion  of  liquids  is  small,  and  the  specific  heat  of 
the  liquid  is  taken  to  represent  the  combined  quantities  A,  B,  and 
c.  The  quantity  of  heat  necessary  to  raise  the  temperature  of 
1  Ib.  of  water  from  the  melting-point  of  ice  to  the  boiling-point 
of  water  being 

q  =  c  x  212° 
and  through  any  given  range  of  temperature 

q  =  c  x  (ti-  t) 

c  being  the  mean  specific  heat  for  the  given  range  of  tempera- 
ture, and  ti—  t,  the  number  of  degrees. 

125.  Latent  Heat  of  Vaporization.  —  At  the  boiling-point  of 
a  liquid,  another  remarkable  phenomenon  occurs,  similar  to  that 
attending  the  melting  of  the  body.     The  term  A  again  van- 
ishes, or,  in  other  language,  the  temperature  of  the  liquid  and 
its  vapor  remains  constant,  as  long  as  the  external  pressure  is 
constant,  until  ajl  the  liquid  has  passed  to  the  state  of  vapor. 
All  the  heat  transferred  to  the  substance  during  this  transfor- 
mation becomes  latent,  or  is  expended  in  producing  the  work 
represented  by  B  +  c. 

The  sum  of  these  two  quantities  expressed  in  units  of  heat  or 

T>     |     r\ 

case  *^e  (luan^ty  which  has  received  the  name 


of  latent  heat  of  evaporation,  and  which  has  been  determined 
by  various  investigators  for  different  liquids  and  for  different 
boiling-points.  The  following  table  gives  the  latent  heats  of 
evaporation,  in  English  units,  of  various  substances,  the  pres- 
sure on  the  external  surface  being  one  atmosphere. 


58  HEAT. 

Latent  heat  of  Vaporization,  in  English  units,  at  one  atmo- 

sphere. 
Water  ............  966.23  .  .  .Eegnault. 

Ether  .............  164.0   .  .  .Favre  and  Silberman. 

Oil  of  turpentine  .  .  .  123.0  ____      "  " 

Alcohol  ...........  372.7....       "  " 

Hydrocarbons  ......  107.8  ____       "  " 

The  change  from  the  state  of  liquid  to  the  state  of  vapor 
being  accompanied,  at  the  pressures  most  employed,  by  a  con- 

siderable increase  of  volume,  the  term  —  -  in  the  general  forum- 

T>  r\ 

la  ^r^+T^r-,  which  represents  the  latent  heat  of  vaporization, 


becomes  appreciable.     The  term  —  —  represents  the  heat  em- 

ployed in  overcoming  the  attractions  of  the  particles,  by  which 
they  are  entirely  removed  from  attractive  influence  on  each 
other;  this  constitutes  the  principal  part  of  the  latent  heat. 

fl 

While  the  term  —  -  represents  the  work  of  overcoming  the 

77.4 

external  pressure  in  units  of  heat,  and  may  be  represented  by 

P   TJ 

r,  P  representing  the  external  pressure,  and  r  the  increase 


of  volume  which  the  liquid  undergoes  in  expanding  to  the  va- 
porous form  ;  so  that  if  L  represents  the  total  latent  heat,  or 

T>  —  L  r\ 

--—--,  in  units  of  heat,  we  may  represent  this  by 


PU 


L  B     .,. 

E  representing  the  units  of  heat  corresponding  to  ==~. 

126.  The  latent  heat  of  vaporization  of  water  for  different  tem- 
peratures or  pressures,  to  about  375°  Fahr.,  was  determined  by 
Regnault,  in  a  series  of  experiments  no  less  important  and 
valuable  than  those  made  by  this  celebrated  physicist  for  de- 
termining the  relation  between  the  temperatures  and  pressures. 

Rankine  gives  the  following  empirical  formula,  based  on  that 
of  Regnault,  which  represents  the  results  of  these  experiments  : 


HEAT.  59 

L  =  1091.T-0.695  (t-32°)-0.000000103  (t-39.10)3 
or,  approximately  for  technical  applications, 

L  =  1092.-0.7  (t-32°) 
=  966-O.r  (t-212°) 

From  this  formula  it  is  apparent  that  the  latent  heat  of  evapo- 
ration for  water  diminishes  with  the  temperature  above  212°. 

127.  Total  Heat  of  Vaporization. — The  total  heat  necessary 
to  transform  one  pound  of  water  from  the  liquid  condition  at  the 
melting-point  of   ice   to  the   condition  of  saturated  vapor  or 
steam  at  the  temperature  t,  may  now  be  estimated.      This  is 
called  the  total  heat  of  vaporization,  and  represents  the  sum 
of  the  heat  which  is  required  to  heat  the  water  from  the  tem- 
perature 32°  to  the  temperature  t,  and  the  heat  which  disap- 
pears as  latent  heat.     By  algebraic  symbols  this  sum  is  evidently 
expressed  as  follows : 

Q  =  c  (t  —  32°)  +  L  =  q  +  L 

c  being  the  mean  specific  heat  of  water  between  the  limits  of 
temperature,  and  L  the  latent  heat  of  vaporization  at  the  higher 
temperature. 

128.  The  results  of  Regnaulfs  experiments,  already  referred 
to,  led  him  to  the  discovery  that  the  total  heat  of  the  vapor  of 
water  from  the  temperature  of  melting  ice  increases  at  a  uni- 
form rate  as  the  temperature  rises. 

Begnault's  formula   by  which  this  law  is  expressed  is  as 
follows : 

Q  =  606.5  +  0.305  t 

Q  being  the  total  heat  in  calories,  and  t  being  expressed  in  Centi- 
grade degrees. 

The  equivalent  English  formula  is— 

Q  =  1091.7  +  0.305.  (t-32°) 
The  expression  for  the  total  heat  of  vaporization  is — 

Q  =  q  +  L 
from  which  we  have          L  —  Q  —  q 

that  is,  the  latent  heat  of  vaporization  is  equal  to  the  total  heat, 
diminished  by  the  quantity  of  heat  necessary  to  raise  the  tem- 
perature of  the  liquid  from  the  melting-point  of  ice  to  the  final 
temperature  of  evaporation. 


60  HEAT. 

In  practice  the  specific  heat  of  liquid  water  may  often  be 
regarded  as  unity,  and  q  for  1  Ib.  of  water  will  then  be  repre- 
sented by  1  x  (ti  —  t),  or  (tt  —  t)  the  difference  of  temperatures. 

The  above  formula  for  the  total  heat  gives  the  total  heat 
necessary  to  raise  the  temperature  of  1  Ib.  of  water  from  32°  to 
any  temperature  and  evaporate  it  at  that  temperature.  Water 
is  not  usually  obtained  in  industrial  processes  at  so  low  a  tem- 
perature as  32°  (e.g.,  the  feed-water  of  steam-boilers),  and  is 
often  heated,  by  what  would  otherwise  be  wasted  heat,  to  a  tem- 
perature as  high  as  possible,  before  its  introduction  to  the 
evaporating  vessel. 

If  from  the  total  heat  as  given  above  by  the  formula 

Q  =  1091.7   +  0.305  (t  —  32°) 

we  subtract  the  heat  necessary  to  raise  1  Ib.  of  water  from  32° 
to  the  temperature  of  the  feed- water  t±  we  shall  have  the  total 
heat  required  to  raise  the  water  from  the  temperature  ^  to  t, 
and  evaporate  it  at  t°  Fahr. 

Q  =  1091.7   +  0.305  (t  -  32)  -  c  (tx  -  32) 

c  being  the  mean  specific  heat  of  water  between  32°  and  ^  or, 
approximately,  c  being  1,  the  formula  may  be  written — 

Q  =  1092.  +  .3  (t  -  32)— (ti  -  32) 

129.  Factor  of  Evaporation.— In  experiments  to  determine 
the  evaporative  powers  of  given  kinds  of  fuel,  or  of  given  boilers, 
for  the  purposes  of  comparison,  it  is  necessary  to  refer  all  such 
experiments  to  the  same  standard  conditions  ;  and  it  is  usual  to 
select  the  condition  of  water  supplied  to  a  boiler  at  212°  Fahr. 
and  evaporated  at  that  temperature ;  at  which  the  number  of 
units  of  heat  necessary  for  each  Ib.  is  966.  If  the  water  is  actu- 
ally supplied  at  a  lower  temperature,  and  evaporated  at  a  higher 
temperature,  the  quantity  of  water  which  would  have  been 
evaporated  under  the  standard  conditions  of  temperature,  i.e., 
from  and  at  212°,  by  the  same  quantity  of  fuel  burned,  may  be 
found  by  a  simple  proportion,  thus  : 

Let  Wx  be  the  weight  of  water  actually  evaporated  at  the 
higher  temperature  by  the  total  heat  Qt  found  by  the  above  for- 
mula, and  x  the  quantity  which  would  have  been  evaporated 
if  the  water  had  been  supplied  and  evaporated  at  212°.  Then 
we  shall  have,  evidently, 


HEAT.  61 

x  966  ^  Wl      Qt 

and  x    =  w,  — -^— 

L    966 

The  following  formula  for  the  factor  ™  for  any  tempera- 
ture ti  of  the  feed-water  and  any  other  temperature  t  of  the 
evaporating  point,  is  given  by  Rankine : 


130.  Total  Heat  of  Superheated  Steam. — When  dry  satu- 
rated steam  is  superheated,  it  is  evident,  from  what  precedes, 
that  the  additional  quantity  of  heat  necessary  to  raise  the  tem- 
perature of  1  lb.,  the  steam  1°  will  depend  on  the  specific  heat 
of  steam.  This,  as  determined  by  Regnault,  is  0.475,  and  to  heat 
saturated  steam  from  the  temperature  t,  its  boiling-point,  under 
a  given  pressure,  to  a  temperature  t2  under  the  same  constant 
pressure,  will  be. 0.475  (ta  -  t). 

So  that  the  total  heat  of  superheated  steam  may  be  found  by 
the  formula — 

q=    1091.7  +  0.305  (t  -  32) +  0.475  (t2  -  t) 

The  total  quantity  of  heat  in  English  units  necessary  to  raise 
the  temperature  of  1  lb.  of  water  from  32°  to  a  given  tempera- 
ture and  evaporate  it  at  that  temperature  has  been  given  in  the 
form  Q  —  q  +  z,  from  which  we  have  z  =  Q-q,  in  which  q 
represents  the  quantity  of  heat  required  to  raise  the  •  tempera- 
ture of  the  liquid  f rom  32°  to  the  given  temperature  and  z 
the  quantity  necessary  to  evaporate  it  at  that  temperature,  or  the 
latent  heat  of  vaporization.  It  has  been  also  stated  that  the 
quantity  z  is  really  composed  of  two  terms, 

p  IT 

L    =  E   + 


772 

in  which  K  represents  that  part  of  the  latent  heat  which  arises 
from  the  work  of  the  heat  in  overcoming  completely  the  molec- 

"P     TT 

ular  attractions,  and  =      tnat  Pai>t  which  arises  from  the  work 


performed  in  the  expansion  of  the  volume  of  the  liquid  to  the 


62  HEAT. 

volume  of  the  liquid  and  its  vapor  ;  the  increase  of  volume  being 
represented  by  u  and  the  external  pressure  by  P.  The  total 
quantity  of  heat  required  to  raise  1  Ib.  of  water  from  32°  to  any 
temperature,  and  evaporate  it  at  that  temperature,  will  then  be 
expressed  by 

p  u 


In  this  expression  q  may  be  said  to  be  the  quantity  of  heat 
contained  in  the  water  at  the  temperature  of  vaporization, 

p  u 

R  the  quantity  of  heat  contained  in  the  vapor,  and   -^=77  a 

77^ 

quantity  of  heat  which  has  been  converted  into  external  work. 

131.  The  separation  of  the  latent  heat  of  vaporization  into  its 
two  parts,  and  the  determination  of  the  values  of  these  parts,  is 
due  to  Prof.  Zeuner,  whose  researches  in  this  subject  have  sim- 
plified greatly  the  mathematical  theory  of  the  mechanical  action 
of  steam  in  its  employment  in  the  steam-engine. 

Prof.  Zeuner  calls  the  quantity  q  the  heat  of  the  liquid,  the 

P  TJ 

quantity  R  the  internal  latent  heat,  and  the  quantity  the 


external  latent  heat. 

If  from  the  total  quantity  of  heat  Q  we  subtract  the  quantity 

f==^  we  shall  have  j  =  Q  —.7/^0"  which  is  designated  by  Prof.  Zeu- 


ner, the  heat  of  the  vapor.  Its  value  indicates  the  excess  in 
units  of  heat  of  the  heat  contained  in  unit  of  weight  of 
the  vapor,  over  the  heat  contained  in  the  unit  of  weight  of  the 
liquid  at  32°  fahr.  from  which  it  was  produced. 

The  heat  of  the  vapor  j  and  the  internal  latent  heat  R  =  L 

P   TJ 

—  ==     are   independent  of  the  mode  of  evaporation,  while  in 


employing  thte  total  heat  of  vaporization  Q,  and  the  latent  heat 
of  evaporization  L  in  the  ordinary  mode,  it  is  necessary  to  suppose 
that  the  evaporation  takes  place  under  constant  pressure  •.* 

The  quantities  j  and  R  are  related  to  each  other  according 
to  the  last  two  expressions  by  the  formula 

q  =  j  —  R 
because  we  have  from  these  expressions 

*  Zeuner,  de  la  Chaleur. 


HEAT.  63 

J  —   K  =  Q  —  L 

and  from  a  preceding  formula 

q  —  Q  —  L 

p  u 
The  quantity  -==    in  the  preceding  formulas   might  be  cal- 


culated from  the  formula  of-Mariotte  and  Gay-Lussac:  P  u  = 
K  T  for  any  temperature  t,  or  any  absolute  temperature  T,  if 
vapors  were  strictly  subject  to  the  law  of  perfect  gases  ;  but  as 
this  formula  cannot  be  applied,  Prof.  Zeuner  employs  another 
formula,  based  on  the  dynamic  theory  of  heat,  by  which  the  value 

p  u 
of  7==~  is  found,  and  in  which  the  values  of  L,  the  total  latent 

77^ 

of  evaporation,  are  taken  from  the  experiments  of  Regnault. 

The  values  of  this  term  having  been  found  for  different 
pressures  and  temperatures,  if  these  values  be  subtracted  from 
the  total  latent  heat  L,  the  results  will  give  the  corresponding 
values  of  R. 

132.  Table  XV.,  pp.  64,  65,  exhibits  the  results  of  calculations 

P  TJ 

made  by  Prof.  Zeuner  to  determine  the  values  of  K  and  -==^  in 


the  manner  indicated  for  different  pressures,  from  1  to  14  at- 
mospheres, for  the  vapor  of  water. 

The  same  table  contains  the  corresponding  values  of  the. 
quantity  q,  the  heat  of  the  liquid. 

The  table  of  Prof.  Zeuner  has  been  transformed  from 
Centigrade  to  Fahr.  and  from  French  to  English  units,  and  the 
quantities  given  in  the  table  refer  to  1  Ib.  and  one  cubic  foot 
as  the  units  of  weight  and  volume. 

The  numbers  in  this  table  give  the  numerical  values  of  the 
terms  of  the  equation 

p  u 


for  1  Ib.  of  water  and  for  different  temperatures. 

133.  Total  Heat  in  Wet  Steam.—  The  quantity  of  heat  con- 
tained in  a  mixture  of  liquid  and  vapor,  whether  the  liquid  be 
mechanically  suspended  in  the  form  of  minute  drops,  constituting 
wet  stecim,  or  whether  the  liquid  remain  in  a  mass  at  the  bottom 
of  the  vessel,  may  be  found,  if  the  relative  quantities  of  liquid 
and  vapor  can  be  determined.  If  x  be  the  weight  of  vapor 
in  1  Ib.  of  the  mixture,  the  quantity  of  heat  in  the  liquid  at  the 


64: 


HEAT. 


TABLE  XV. 

Giving  the  heat  of  the  liquid,  the  internal  latent  Jieat,  the  external  latent  heat, 
the  specific  volume  and  specific  weight  of  1  Ib.  of  saturated  steam  at  different 
pressures. 


Pressure 
in  atmos- 
pheres. 

Pressure 
in  Ibs.  per 
sq.  inch. 

Tempera- 
ture in 
degrees 
Pahr. 

Heat  of 
liquid  in 
units  of 
heat. 

q. 

Latent  in- 
ternal heat 
of  vapor  in 
units  of 
heat. 
R. 

External 
latent  heat 
in  units  of 
heat. 

P  XT 

772 

Specific 
volume  in 
cu.  feet. 

U. 

Specific 
weight  in 
Ibs. 

D. 

0.1 

1.47 

115.0 

83.308 

969.926 

63.835 

233.0879 

.0043 

0.2 

2.94 

141.0 

109.060 

949.651 

66.175 

120.8162 

.0083 

0.3 

4.41 

157.0 

125.437 

936.779 

67.633 

82.3180 

.0121 

0.4 

5.88 

169.4 

137.698 

927.155 

68.708 

62.7204 

.0159 

0.5 

7.35 

178.9 

147.631 

Q19.381 

69.547 

50.7880 

.0197 

0.6 

8.82 

187.6 

155.992 

912.818 

70.281 

42.7705 

.0234 

0.7 

10.29 

194.6 

163.267 

907.123 

70.897 

36.9812 

.0270 

0.8 

11.76 

201.8 

169.747 

902.054 

71.438 

32.6065 

.0307 

0.9 

13.23 

206.8 

175.577 

897.498 

71.923 

29.1800 

.0343 

.0 

14.70 

212.0 

180,900 

893.340 

72.360 

26.4216 

.0378 

.1 

16.17 

216.8 

185.789 

889.524 

72.758 

24.1517 

.0414 

.2 

17.64 

221.4 

190.332 

885.978 

73.127 

22.2519 

.0449 

.3 

19.11 

225.6 

194.587 

882.661 

73.469 

20.6356 

.0484 

.4 

20.58 

229.5 

198.569 

879.557 

73.787 

19.2451 

.0519 

.5 

22.05 

233.1 

202.334 

876.625 

74.086 

18.0341 

.0554 

1.6 

23.52 

236.6 

205.900 

873.848 

74.367 

16.9720 

.0589 

1.7 

24.99 

240.0 

209.284 

871.214 

74.633 

16.0301 

.0623 

1.8 

26.46 

243.2 

212.506 

868.709 

74.884 

15.1907 

.0658 

1.9 

27.93 

246.2 

215.602 

866.302 

75.121 

14.4362 

.0692 

2.0 

29.40 

249.1 

218.551 

864.009 

75.350 

13.7570 

.0726 

2.1 

30.87 

251.9 

221.391 

861.802 

75.566 

13.1387 

.0760 

2.2 

32.34 

254.5 

224.123 

859.682 

75.773 

12.5764 

.0794 

2.3 

33.81 

257.1 

226.746 

857.646 

75.973 

12.0606 

.0828 

2.4 

35.28 

259.6 

229.295 

855.666 

76.165 

11.5881 

.0862 

2.5 

36.75 

262  0 

231.755 

853.758 

76.349 

11.1508 

.0896 

2.6 

38.22 

264.4 

234.142 

851.908 

76.527 

10.7471 

.0929 

2.7 

39.69 

266.6 

236.437 

850.127 

76.698 

10.3722 

.0963 

2.8 

41.16 

268.8 

238.678 

848.390 

76.864 

10.0230 

.0996 

2.9 

42.63 

271.0 

240.865 

846.697 

77.024 

9.6978 

.1029 

3.0 

44.10 

273.1 

242.980 

845.052 

77.177 

9.3935 

.1063 

3.1 

45.57 

275.0 

245.039 

843.464 

77.328 

9.1084 

.1096 

3.2 

47.04 

277.0 

247.045 

841.912 

77.472 

8.8392 

.1129 

3.3 

48.51 

278.9 

249.014 

840.389 

77.614 

8.5877 

.1162 

3.4 

49.98 

280.8 

250.927 

838.908 

77.753 

8.3507 

.1195 

3.5 

51.45 

282.6 

252.788 

837.470 

77.884 

8.1248 

.1228 

3.6 

52.92 

284.4 

254.610 

836.060 

78.016 

7.9133 

.1261 

3.7 

54.39 

286.2 

256.415 

834.665 

78.143 

7.7115 

.1294 

3.8 

55.86 

287.9 

258.149 

833.326 

78.264 

7.5209 

.1327 

3.9 

57.33 

289.6 

259.862 

832.003 

78.386 

7.3383 

.1360 

4.0 

58.80 

291.2 

261.558 

830.693 

78.505 

7.1669 

.1392 

4.1 

60.27 

292.8 

263.200 

829.426 

78.619 

7.0019 

.1425 

4.2 

61.74 

294.4 

264.805 

828.187 

78.730 

6.8449 

.1458 

4.3 

63.21 

295.9 

266.373 

826.976 

78.838 

6.6943 

.1490 

4.4 

64.68 

297.4 

267.943 

825.766 

78.946 

6.5517 

.1523 

4.5 

66.15 

298.9 

269.474 

824.583 

79.052 

6.4140 

.1555 

4.6 

67.62 

300.4 

270.970 

823.432 

79.155 

6.2826 

.1587 

4.7 

69.09 

301.8 

272.448 

822.292 

79.254 

6.1577 

.1620 

HEAT. 
TABLE  XV.— Continued. 


Pressure 
in  atmos- 
pheres. 

Pressure 
in  Ibs.  per 
sq.  inch. 

Tempera- 
ture in 
degrees 
Fahr. 

Heat  of 
liquid  in 
units  of 
heat. 

q, 

Latent  in- 
ternal heat 
of  vapor  in 
units  of 
heat. 
R. 

External 
latent  heat 
in  units  of 
heat. 
PU 

rre 

Specific 
volume  in 
cu.  feet. 

u. 

Specific 
weight  in 
Ibs. 

D. 

4.8 

70.56 

303.2 

273.908 

821.167 

79.353 

6.0359 

.1652 

4.9 

72.03 

304.6 

275.330 

820.071 

79.450 

5.9206 

.1685 

5.0 

73.50 

306.0 

276.734 

818.989 

79.546 

5.8085 

.1717 

5.1 

74.97 

307.4 

278.122 

817.922 

79.637 

5.7011 

.1749 

5.2 

76.44 

308.7 

279.472 

816.881 

79.727 

5.8986 

.1781 

5.3 

77.91 

310.0 

280.822 

815.843 

79.817 

5.4993 

.1813 

5.4 

79.38 

311.3 

282.134 

814.831 

79.905 

5.4032 

.1845 

5.5 

80.85 

312.5 

283.448 

813.821 

79.994 

5.3103 

.1877 

5.6 

82.32 

313.8 

284.726 

812.839 

80.077 

5.1725 

.1909 

5.7 

83.79 

315.0 

285.984 

811.870 

80.159 

5.1341 

.1941 

5.8 

85.26 

316.2 

287.242 

810.902 

80.242 

5.0508 

.1973 

5.9 

86.73 

317.4 

288.466 

809.962 

80.321 

4.9707 

.2005 

6.0 

88.20 

318.6 

289.688 

809.023 

80.401 

4.8922 

.2037 

6.1 

89.67 

319.8 

290.893 

808.097 

80.478 

4.8169 

.2069 

6.2 

91.14 

320.9 

292.059 

807.199 

80.555 

4.7448 

.2101 

6.3 

92.61 

322.0 

293.247 

806.288 

80.629 

4.6727 

.2133 

6.4 

94.08 

323.2 

294.395 

805.406 

80.705 

4.6038 

.2164 

6.5 

95.55 

324.3 

295.526 

804.537 

80.777 

4.5382 

.2196 

6.6 

97.02 

325.4 

296.658 

803.669 

80.849 

4.4725 

.2228 

6.7 

98.49 

326.4 

297.770 

802.814 

80.921 

4.4100 

.2259 

6.8 

9906 

327.5 

298.885 

801.961 

80.989 

4.3491 

.2291 

6.9 

101.43 

328.5 

299.961 

801.135 

81.058 

4.2899 

.2323 

7.0 

102.90 

329.6 

301.037 

800.309 

81.126 

4.2322 

.2354 

7.25 

106.575 

3321 

303.692 

798.273 

81.292 

4.0944 

.2433 

7.50 

110.250 

334.6 

306.256 

796.307 

81.450 

39647 

.2512 

7.75 

113  925 

337.1 

308.763 

794.385 

81.607 

3.8445 

.2590 

8.00 

117.000 

3394 

311.198 

792.520 

81.756 

3.7308 

.2668 

8.25 

121.275 

341.7 

313.598 

790.684 

81.902 

3.6251 

.2747 

8.50 

124950 

344.0 

315.925 

788.904 

82.040 

3.5242 

.2825 

8.75 

128.625 

346.2 

318.195 

787.167 

82.177 

3.4296 

.2903 

9.00 

132  300 

348.4 

320.431 

785.459 

82.309 

3.3399 

.2980 

9.25 

135.975 

350.5 

322.610 

783.792 

82.436 

3.2534 

.3058 

9.50 

139  650 

352.5 

324.734 

782.170 

82.562 

3.1733 

.3135 

9.75 

143  325 

354.6 

326.842 

780.561 

82.683 

3.0965 

.3213 

10.00 

147.000 

356.6 

328.894 

778.995 

82.802 

3.0228 

.3290 

10.25 

150  675 

358.5 

330.890 

777.470 

82.915 

2.9539 

.3367 

10.50 

154.350 

360.4 

332.869 

775.962 

83.029 

2.8866 

.3444 

10.75 

158.025 

3623 

334.809 

774.481 

83.140 

2.8241 

.3521 

11.00 

161.700 

364.1 

336.717 

773.028 

83.245 

2.7633 

.3598 

11.25 

165  375 

365.9 

338.603 

771.590 

83.351 

2.7056 

.3675 

11.50 

109  050 

367.7 

340.436 

770.195 

83.452 

2.6495 

.3751 

11.75 

172.725 

369.4 

342.250 

768.814 

83.551 

2.5967 

.3828 

12.00 

170.400 

371.2 

344.027 

767.462 

83.648 

2.5454 

.3904 

12.25 

180  075 

372.  § 

345.787 

766.123 

83.743 

2.4957 

.3981 

12.50 

183  750 

374.5 

347.508 

764.813 

83.837 

2.4493 

.4057 

12.75 

187.425 

376.1 

349.213 

763.555 

83.927 

2.4028 

.4133 

13.00 

191.100 

377.8 

350.899 

762.237 

84.017 

2.3596 

.4209 

13.25 

194.775 

379.4 

352.548 

760.984 

84.103 

2.3179 

.4285 

13.50 

198  450 

380.9 

354.179 

759.744 

84.190 

2.2763 

.4361 

13.75 

202.125 

382.5 

355.792 

758.520 

84.272 

2.2378 

.4437 

14.00 

205.800 

384.0 

357.367 

757.325 

84.355 

2.1994 

.4512 

66  HEAT. 

temperature  of  vaporization  will  evidently  be  q,  and  R  being 
the  latent  internal  heat  of  1  Ib.  of  vapor,  x  R  will  be  the  latent 
internal  heat  of  the  quantity  of  vapor  x  ;  hence  the  total  heat 
in  the  mixture  will  be — 

Qi  =  q  +  R  x 

the  quantities  q  and  R  being  found  from  the  table. 

The  usual  method  of  determining  the  total  heat  of  wet 
steam  has  been  to  regard  the  total  latent  heat  of  the  vapor  as 
contained  in  the  steam,  and  to  employ  the  formula — 

Q!=  N  q  +  N!  L 

=  N  (t  -  32°)  -h   Nl(l091.7  +  0.305  (t  -  32°) 

N  being  the  number  of  Ibs.  of  water,  and  NJ.  the  number  of  Ibs. 
of  vapor  in  the  mixture ;  the  specific  heat  of  water  being  1,  and 
the  initial  temperature  being  32°. 

The  difference  between  this  formula  and  the  last,  from  which 
we  have — 

(N  -h  Ni)  Q!  =  (N  +  NL)  (q  +  R  x) 

being  that  the  internal  latent  heat  of  the  vapor,  only,  is  con- 
sidered, N  +  N!  being  the  total  weight  of  liquid  and  vapor. 

"P  TT 

134.  The  values  of  Q  =  q  +  R  +  — —  found  from  the  tables, 

conform  to  the  law  of  Regnault,  that  the  total  heat  increases 
uniformly  as  the  temperature  rises. 

The  amount  of  this  increase  is  small  even  for  a  great  range 
of  temperature.  For  instance,  the  total  heat  necessary  to  raise 
a  Ib.  of  water  from  32°  to  212°,  and  evaporate  it  at  that  tem- 
perature, is  1146.6  units  of  heat :  and  the  quantity  necessary 
to  raise  the  same  amount  of  water  from  32°  to  329,5°  Fahr. 
(corresponding  to  7  atmospheres),  and  evaporate  it  at  that  tem- 
perature, is  only  1182.47,  or  35.9  additional  units  of  heat ;  less 
than  ^g-  part  of  the  latent  heat  of  evaporation  of  1  Ib.  of  water 
at  212°. 

The  values  of  z,  the  latent  heat  of  evaporation,  may  be  found 
from  the  table,  for  any  given  pressure  or  temperature,  by  adding 

T*   TT 

together  the  corresponding  values  of  R  and  -=. 


HEAT.  67 

DENSITY  OF  GASES  AND  VAPORS. 

135.  The  term  density  refers  to  the  degree  of  approximation 
of  the  particles  of  a  body  to  each  other.     It  becomes  specific 
when  it  refers  to  the  number  of  molecules  or  atoms  in  a  unit  of 
volume  of  a  given  substance,  this  unit  being  a  standard  for  all 
bodies.     In  English  measures,  one  cubic  foot  is  the  standard 
unit  of  volume,  and  the  weight  of  a  cubic  foot  of  a  substance 
in  any  condition  is  the  specific  weight  of  that  substance  in  that 
condition.     It  is  usual  to  express  specific  weights  in  terms  of 
the  weight  of  a  unit  of  volume  of  a  standard  substance,  the 
latter  weight  being  taken  as  unity.    Water  is  the  general  stand- 
ard for  specific  weights,  but  for  gases  and  vapors  air  is  also  taken 
as  a  standard,  the  weight  of  one  cubic  foot  of  air  being  unity. 

The  following  table  shows  the  relative  densities  at  32°  Fahr. 
and  one  atmosphere  pressure,  of  some  of  the  gases  commonly 
met  with : 

XVI.  Relative  Densities. 

Air 1.00000         Water 1.0000000 

Nitrogen 0.97137        Air 0.0012932 

Hydrogen 0.06926         Nitrogen 0.0012562 

Oxygen 1.10563         Hydrogen 0.0000896 

Carbonic  Acid 1.52901         Oxygen 0.0014298 

Carbonic  Acid.  .0.0019774 

136.  The  following  are  the  weights  of  one  cubic  foot  of  each 
of  the  same  substances  in  pounds  avoirdupois,  under  the  same 
conditions,  viz.,  at  32°  F.  and  one  atmosphere  pressure,  except 
for  water,  which  is  taken  at  39.1°  Fahr. : 

XVII.  Weight  in  pounds  Avoirdupois  of\  cu.foot. 

Water 62.425 

Air. 0.08073 

Nitrogen 0.07860 

Hydrogen 0.00559 

Oxygen 0.08926 

Carbonic  Acid 0.12344 

Steam 0.0502 

137.  The  density  of  a  perfect  gas,  at  any  other  pressure  and 
temperature,  may  be  found  from  the  law  of  Mariotte  and  Gay- 
Lussac. 


68  HEAT. 

In  the  expression 

p  v  =  K  T 

v  may  be  taken  as  the  volume  of  unit  of  weight  or  specific 
volume,  and  if  d  represent  the  weight  of  unit  of  volume  or 

specific  weight,  we  shall  have  v  D  =  i  and  v  = — 

hence  JP 

D 

-r> 

and  for  any  other  pressure  and  temperature — -  =  K  T! 
From  these  two  equations  we  obtain  by  division — 

P.      Di  T 


and  L»I    =      D.  —     • — 

PI        T! 

The  density  here  considered,  being  the  specific  weight,  or 
wreight  of  a  unit  of  volume,  may  be  found  in  the  above  table, 
headed,  weight  in  pounds  avoirdupois  of  one  cubic  foot,  for 
any  perfect  gas  mentioned  in  the  table. 

138.  The  specific  volume  of  a  gas  is  the  volume  of  unit  of 
weight.    In  English  measures  one  pound  avoirdupois  is  the  unit 

of  weight,  and  to  obtain  the  specific  volume  we  have  v  =  —  the 
reciprocal  of  the  specific  weight. 

Specific  volumes,  or  volumes  of  one  pound  of  each  of  the 
substances  named,  are  given  below  in  cubic  feet,  for  32°  Fahr. 
and  one  atmosphere : 

Air 12.3870 

Nitrogen 12.7226 

Hydrogen 178.8909 

Oxygen 11.2032 

Garb.  Acid. 8.1011 

Steam 19.9203 

139.  If  saturated  vapors  could  be  treated  as  perfect  gases,  the 
following  formulas  for  determining  the  specific  volumes  and 
specific  weights  of  the  vapor  of  water  might  be  employed : 

p  v  =  KT 


HEAT.  69 

in  which,  for  English  measures,  p  is  the  pressure  in  pounds  per 
square  foot,  v  the  volume  of  one  pound ;  K  is  a  constant  equal 
to  85.766,  and  T  the  absolute  temperature.  The  constant  85.766 
is  derived  from  the  corresponding  value  of  u  for  air,  on  the 
supposition  that  the  weight  of  1  cubic  foot  of  saturated  steam 
is  0.622  that  of  air  at  the  same  temperature  and  pressure. 
From  the  above  formula  we  have  for  saturated  steam — 

PV  =  85.766  XT 

85.766  XT 
v  = 


1 

D  =  -    - 


v       85.766  XT 

Let  it  be  required,  for  instance,  to  determine  the  volume  of 
1  pound  of  saturated  steam  at  a  pressure  of  6  atmospheres. 
This  pressure  corresponds  to  a  temperature  Fahr.  of  318.6, 
and  the  corresponding  absolute  temperature  will  be  459.4 
+  318.6  =  778°  Fahr.  Six  atmospheres  pressure  is  12700.8 
pounds  per  square  foot,  and  the  formula  becomes,  for  the  spe- 
cific volume, 

85.766x778  . 

Vr        12700.8        =  5-253  cu.  feet, 

arid  for  the  specific  weight, 


It  has  been  remarked,  however,  that  for  saturated  vapors  the 
law  of  Mariotte  is  strictly  applicable  only  on  the  supposition 
that  the  vapor  is  in  the  superheated  condition. 

In  order  that  this  law  may  be  applicable,  it  is  necessary  that 
the  specific  weight  of  vapor  shall  bear  a  constant  ratio  to  that 
of  air  at  the  same  pressure  and  temperature.  This  ratio,  as 
determined  by  Regnault  for  saturated  steam,  is  0.622.  The 
following  table  gives  the  ratios  of  the  weights  of  unit  of  volume 
of  the  vapor  of  water,  relative  to  air,  for  increasing  pressures, 
as  determined  by  Zeuner  theoretically  : 


70  HEAT. 

Pressure  of  the  saturated  vapor  Density  of  vapor 

in  atmospheres.  relative  to  air. 

0.1  ...........................  0.621 

0.5  ...........................  0.633 

1  ...............  .  ............  0.640 

2  ............................  0.648 

5  ............................  0.662 

10  ...................  .........  0.676 

From  this  table  it  will  be  seen  that  it  is  only  at  very  low 
pressures  that  the  law  of  Mariotte  and  Gay-Lussac  will  apply 
to  saturated  vapors.  For  pressures  such  as  are  ordinarily  em- 
ployed in  the  steam-engine  the  law  does  not  apply. 

140.  A  knowledge  of  the  specific  volumes  and  specific  weights 
of  saturated  vapors,  especially  of  the  vapor  of  water,  is  of  great 
importance,  in  technical  applications,  for  the  pressures  and  tem- 
peratures usually  employed  ;  and  until  the  direct  experiments 
of  Fairbairn  and  Tate  were  made  to  determine  these  quantities, 
reliance  was  placed,  to  a  great  extent,  on  the  law  of  Mariotte 
and  Gay-Lussac.     These  experiments  indicated  a  different  law, 
and  one  which  corresponds  perfectly  with  the  dynamic  theory 
of  heat. 

p  u 

141.  The  quantity  ==^  in  Table  XY.  furnishes  the  means  of 


ascertaining  directly  the  specific  volume  —  the  column  headed  u 
giving  the  volume  of  the  saturated  vapor  from  1  Ib.  of  water 
for  different  temperatures  and  pressures.  Strictly  speaking, 
the  values  of  u  in  this  table  designate  the  difference  between 
the  volume  of  the  vapor  of  1  Ib.  of  water  and  the  volume  of  the 
water  from  which  it  was  produced  ;  or, 


ui  being  the  real  specific  volume  of  the  vapor,  and  Vj.  the  volume 
of  one  pound  of  water. 

From  which  we  have  the  real  specific  volume 


=  TJ 


v1?  the  volume  of  1  Ib.  of  water,  which  may  be  regarded  as 
constant  for  all  temperatures,  is  .016  of  a  cubic  foot,  and  hence 

Ui  =  u  +  0.016  cubic  feet 
the  value  of  u  being  taken  from  Table  XY. 


HEAT.  71 

The  specific  weight  will  then  be 

1 


D  = 


U  4-  Vi 


The  values  of  the  specific  weights  of  the  vapor  of  water  cal- 
culated in  this  manner,,  are  found  in  the  table  in  the  column 
headed  D. 

These  numbers  will  be  found  to  correspond  closely  with  those 
of  Fairbairn  in  Table  VIII.  of  his  "  Mills  and  Millwork,"  for 
the  same  temperature  —  Fairbaim's  table  having  been  con- 
structed from  formulas  based  on  his  experiments. 

142.  Prof.  Zeuner  gives  an  empirical  formula  for  D,  which  is 
as  follows  : 


D  =  apn 
in  which  D  is  expressed  in  kilogrammes  a  =  0.6061  and  —  = 

0.9393. 

Referring  to  the  example  which  has  just  been  given,  tne 
volume  v  of  1  Ib.  of  saturated  steam  at  the  pressure  of  6  atmos- 
pheres is,  from  the  table, 

N!  =  N  +  Y!  =  4.8922  -f  016  =  4.908  cubic  feet. 

The  value  calculated  by  Mariotte  and  Gay-Lussac's  law, 
D  being  0.622  of  air,  is  5.266  cubic  feet. 

The  value  of  D  by  Zeuner's  table  is  0.2037  Ibs. 
The  value  calculated  by  Mariotte's  law,  0.1903  Ibs. 
It  appears  evident  that  if  Mariotte  and  Gay-Lussac's  law  is 
to  be  applied  to  saturated  vapors,  the  relative  density  of  steam 
is  not  to  be  regarded  as  constant,  but  as  varying  according  to 
the  preceding  table,  page  70. 

If,  in  the  example  given,  the  density  of  the  steam  be  taken 
at  0.662,  the  density  of  air  at  6  atmospheres,  the  application  of 
this  law  will  give 

p  v  =  80.470  T. 

and  v  =  4.929  cubic  feet. 

v  =  4.908  by  the  table. 
D  —     .2025  by  the  formula  above. 
D  =     .2037  by  the  tables. 

Fairbairn  gives  a  formula  for  what  he  calls  the  "  specific 


72  HEAT. 

volume,"  equivalent  to  the  following,  p  being  expressed  in  Ibs. 
per  square  inch  : 

24317.5 


v  =  25.62  + 


p  +  0.365 


This  volume,  however,  is  the  ratio "  of  the  volume  of  the 
liquid  to  the  volume  of  vapor  that  it  will  produce  at  the  pres- 
sure P.  A  table  of  these  ratios  for  different  pressures  may  be 
found  in  Fairbairn's  work. 

Zeuner's  tables  of  specific  volumes  and  specific  weights  are 
theoretical,  being  based  on  the  dynamic  theory  of  heat,  and 
Regnault's  tables  for  temperatures  and  pressures,  wThile  Fair- 
bairn's  tables  for  the  same  quantities  are  based  on  his  direct 
experiments. 

To  find  the  real  specific  volume  from  that  designated  by 
Fairbairn  as  the  "specific  volume,"  it  is  only  necessary  to 
multiply  the  "specific  volumes"  of  his  table  by  0.016,  the 
volume  of  one  pound  of  water. 


r    7    I  >    |>     \     i>   \' 
lj  I    1>  it  A    i\    Y 

U  X  1  V  E  Li  S  I T  Y   O  F 

CALIFORNIA 


CHAPTER 


COMBUSTION. 

143.  CHEMICAL  action  when  accompanied  by  the  development 
of  light  and  heat  is  usually  called  combustion. 

144.  Inflammation  denotes  that  kind  of  combustion  in  which 
the  products  are  gaseous  and  flame  is  produced. 

145.  Ignition  is  simply  the  incandescence  of  a  body  unat- 
tended by  chemical  change.* 

146.  The  phenomena  of  heat  being  those  of  rapid  molecular 
motions,  the  heat  and  light  developed  by  combustion  must 
indicate  an  increased  molecular  movement  in  the  particles  of 
bodies,  when  combustion  takes  place,  proportional  to  the  amount 
or  force  of  the  chemical  attractions. 

147.  The  heat  of  combustion  may  therefore  be  rationally  ex- 
plained by  saying  that  intense  and  violent  increase  of  motion 
in  the  particles  of  the  compound  is  produced  by  the  chemical 
attractions. 

148.  Ordinary  combustion  consists  in  the  combination  of  ox- 
ygen with  various  substances  :  the  temperature  required  being 
different  for  different  substances,  and   varying  for  the  same 
substance  with  the  rapidity  of   the  combustion.     Phosphorus 
combines  slowly  with  oxygen  at  77°  F.  ;  charcoal  burns  slowly^ 
but  does  not  ignite,  below  a  red-heat  ;  sulphur  burns  in  air  at 
about  550°  F. 

But  most  elementary  substances  require  to  be  heated  to  red- 
ness before  combustion  in  oxygen  or  the  air  takes  place. 
According  to  Peclet,  Rolids  emit  light,  or  become  dull  red,  at 
about  750°  F. 

149.  "  Compression  of  air  does  not  appear  to  facilitate  com- 
bustion unless  the  combustion  takes  place  rapidly,"  \  and  is  con- 
sequently attended  with  considerable  evolution  of  heat. 

150.  Most   substances  burn  with   great  rapidity  when  in  a 

*  Watts'  s  Die.  of  Chemistry.  \  Ibid. 


74  COMBUSTION. 

finely-divided  state.  Fine  dust  of  many  substances  burns  in 
this  manner  with  a  rapidity  which,  in  a  closed  space,  may  give 
rise  to  such  a  degree  of  pressure,  from  the  expansion  of  the 
gases,  as  to  produce  phenomena  like  explosions.  A  single  spark 
may  thus  produce  instantaneous  combustion  in  a  space  filled 
with  fine  dust. 

151.  Spontaneous  Combustion. — Porous   substances    often 
absorb  and  condense  air  within  their  pores ;  oxidation  begins, 
accompanied  by  an  elevation  of  temperature,  which  accelerates 
the  oxidation  until  the  process  produces  spontaneous  combus- 
tion.    Charcoal  powder,  masses  of  tow,  cotton,  or  rags,  satu- 
rated with  oil,  sawdust  mixed  with  oil,  moist  hay,  and  other 
substances  in  similar  conditions,  have  thus  been  known  to  burst 
into  flame. 

Wood  does  not  take  fire  in  oxygen  gas,  according  to  Thenard, 
at  temperatures  below  about  600°  F. ;  but  if  it  be  long  exposed 
to  a  high  temperature,  even  lower  than  this,  in  air,  it  may 
become  partially  charred,  and  rendered  so  inflammable  as  to 
favor  the  conditions  of  spontaneous  combustion.  Under  such 
conditions,  a  single  spark,  or  accidental  exposure  of  the  sub- 
stance to  a  higher  degree  of  heat,  may  cause  it  to  take  fire. 

Charcoal  from  wood  made  at  a  temperature  of  480°  F.  takes 
fire  in  air  when  heated  to  about  650°  Fahr. 

152.  Ordinary  combustion  is  accompanied,  usually,  by  in- 
candescence  and   flame.      If  a  solid  burns  without  flame,  the 
heat  evolved  at  the  surface  of  contact  of  the  air  and  the  solid 
causes  an  elevation  of  temperature  of  the  residual  solid  particles, 
which  gives  rise  to  a  glow,  or  incandescence,  the  color  and  inten- 
sity of  the  light  being  dependent  on  the  temperature.      Dull 
red  indicates  the  lowest  temperature  at  which  light  appears,  and 
dazzling  white,  the  highest  degrees  of  heat ;  between  these  ex- 
tremes the  light  passes  from  dull  red,  or  cherry  red,  to  bright 
red,  dull  white,  then    to  a  yellowish  and  finally  to   a  bluish 
white,  and  a  full  or  dazzling  white. 

If  the  combustible  is  gaseous,  the  combination  with  oxygen 
may  be  instantaneous,  producing  by  the  violent  concussion  of 
the  air  an  explosion.  In  order  that  the  phenomenon  of  explo- 
sion may  take  place,  the  combustible  gas  must  be  mixed  uni- 
formly with  air,  or  oxygen,  in  the  proper  proportions,  and  then 
heated  to  the  burning-point.  A  similar  effect  takes  place  when 
a  solid  combustible,  such  as  sulphur  or  charcoal,  is  mixed  with 


COMBUSTION.  75 

a  nitrate  or  other  solid  which  gives  up  its  oxygen  readily. 
In  both  cases  it  is  only  necessary  that  the  temperature  be 
raised  to  ignition  at  one  point  by  friction,  percussion,  or  the 
contact  of  a  hot  body,  the  action  being  then  propagated  instan- 
taneously throughout  the  whole  mass. 

When  the  combustion  is  gradual,  the  contact  of  the  combus- 
tible gas  with  oxygen,  or  the  air,  takes  place  usually  at  the 
bounding  surface  of  the  gas ;  as,  for  instance,  when  a  jet  of  gas 
issues  from  an  orifice,  or  when  a  column  of  gas  rises  from  the 
wick  of  a  candle.  The  inner  mass  of  the  combustible  gas  does 
not  ignite  at  first,  and  the  ignited  surface  assumes  the  form  of 
a  hollow  cylinder,  or  cone. 

153.  The  brightness  and  color  of  such  a  flame  depend  not 
only  on  the  degree  of  temperature,  but  upon  the  presence  of 
solid  incandescent  particles  in  the  flame.     These  solid  particles 
arise  sometimes  from  the  compound  produced  by  the  combina- 
tion, but  in  ordinary  forms  of  combustion  of  fuel  they  are  par- 
ticles of  carbon.     Hydrogen  gas,  carbonic  oxide,  alcohol,  and 
sometimes  coal-gas,  burn  thus  with  a  dull  flame. 

A  bright  flame  is  produced  by  compounds  which  contain 
carbon,  from  which  a  portion  of  the  carbon  becomes  separated 
by  the  heat  produced ;  the  separated  particles  being  first  heated 
to  incandescence,  and  afterwards  burned  by  contact  with  the 
air.  If  the  quantity  of  air  supplied  be  not  sufficient,  these 
solid  particles  may  become  cooled  and  form  soot.  The  visible 
part  of  smoke  is  this  soot  cooled  below  red-heat. 

Marsh-gas,  olefiant  gas,  ether,  volatile  oils,  resins,  fats,  etc., 
when  burned,  give  off  carbon  in  this  manner,  and  may  form 
bright  flames,  or  produce,  if  the  separated  particles  are  not  all 
burned,  soot,  or  smoke. 

154.  A  purely  gaseous  substance  does  not  become  luminous 
at  any  degree  of  temperature  however  high  /  luminosity  ~being 
caused  by  particles  of  incandescent  solids  in  the  gas. 

The  combustible  ingredients  of  ordinary  fuel,  and  of  the 
liquids  and  gases  usually  employed  for  the  generation  of  heat, 
are  carbon  and  hydrogen.  These  substances  combine  readily 
with  oxygen,  the  former  producing  by  the  combination  car- 
bonic acid,  or  carbonic  oxide,  and  the  latter  water.  The  oxygen 
required  is  usually  supplied  by  the  atmosphere,  which  contains 
about  one-fifth  of  its  weight  of  this  substance. 

155.  As  a  general  rule,  all  chemical  combinations  produce 


76  COMBUSTION. 

heat,  while  chemical  decompositions  cause  a  disappearance  of 
heat.  In  the  combination  of  two  simple  isolated  elements 
heat  is  evolved  only,  but  where  the  combination  is  effected 
through  the  simultaneous  decomposition  of  compound  substan- 
ces, the  heat  evolved  is  the  resultant  of  that  which  is  produced 
by  the  combination  of  the  combustible  elements,  and  that 
which  disappears  through  the  decompositions. 

In  compounds  containing  oxygen  and  hydrogen  in  the  proper 
proportions  to  form  water,  the  surplus  hydrogen  only  contrib- 
utes to  the  development  of  heat,  when  combustion  takes  place. 

These  elements  combine  to  form  water  in  the  proportion,  by 
weight,  of  one  part  of  hydrogen  to  eight  parts  of  oxygen,  and 
by  volume,  one  of  hydrogen  to  one-half  of  oxygen. 

Carbon  unites  with  oxygen  in  two  proportions,  viz. :  to  form 
carbonic  acid,  six  parts  of  carbon  to  sixteen  of  oxygen,  by 
weight;  and  to  form  carbonic  oxide,  six  of  carbon  to  eight  of 
oxygen.  Carbonic  oxide  is  a  highly  combustible  gas,  taking  up 
when  exposed  to  air  or  oxygen,  at  the  proper  temperature,  eight 
additional  parts,  or  one  equivalent  of  oxygen  to  form  carbonic 
acid. 

Carbon  completely  burned  thus  produces  carbonic  acid  and 
satisfies  the  conditions  of  perfect  combustion.  Imperfectly 
burned,  the  result  usually  of  a  deficiency  of  air,  it  produces  car- 
bonic oxide. 

156.  Composition  of  Atmospheric  Air. — Air  is  composed 
of  oxygen  and  nitrogen.  Ordinary  atmospheric  air  contains 
also,  mechanically,  watery  vapor,  and  carbonic  acid  in  small 
quantities.  Of  these  elements  the  oxygen  alone  is  the  active 
agent  of  combustion. 

Pure  dry  air  contains  oxygen  and  nitrogen  in  the  proportion 
by  weight  of — 

*  Oxygen 0.236 

Nitrogen 0.764 

1.000 
and  by  volume — 

Oxygen 0.213 

Nitrogen 0.7S7 


1.000 


*  Morin  and  Tresca. 


COMBUSTION.  77 

The  weight  of  a  given  quantity  of  air  is  thus  4.25  times  the 
weight  of  oxygen  it  contains,  and  1.31  times  the  weight  of  ni- 
trogen. The  volume  of  a  given  quantity  of  air  is  4.69  times 
the  volume  of  oxygen  it  contains,  and  1.27  times  the  volume  of 


nitrogen. 


One  pound  of  carbon  to  form  carbonic  acid  unites  with  2.66 
pounds  of  oxygen,  the  resultant  weight  being  3.66  pounds  of 
carbonic  acid.  This  requires  11.3  pounds  of  air,  and  produces, 
after  combustion,  12.3  pounds.  Since  one  pound  of  air  occupies 
at  32°  F.  and  at  the  ordinary  pressure  14.7  pounds  per  square 
inch,  12.39  cubic  feet,  it  follows  that  one  pound  of  carbon 
requires,  for  its  combustion,  approximately,  12.39  x  11.3  =  140 
cubic  feet  of  air. 

One  pound  of  carbon  to  form  carbonic  oxide  unites  with  1.33 
pounds  of  oxygen,  making  2.33  pounds  of  carbonic  oxide.  This 
requires  5.65  pounds,  or  about  70  cubic  feet,  of  air  at  ordinary 
temperatures  and  pressures. 

One  pound  of  hydrogen,  to  form  water,  requires  8  pounds 
of  oxygen,  the  resultant  being  9  pounds  of  water.  This  re- 
quires, when  the  combustion  is  in  air,  33.97  pounds,  or  420.0 
cubic  feet  of  air,  and  the  total  weight  after  combustion  is  34.97 
pounds. 

One  pound  of  light  carburetted  hydrogen,  or  marsh-gas,  to 
form  carbonic  acid  and  water,  requires  4  pounds  of  oxygen, 
the  resultant  being  5  pounds  of  carbonic  acid  and  water  in 
the  proportion  of  1  water  to  2.44  carbonic  acid.  For  this  com- 
bustion 17  pounds,  or  approximately  210.0  cubic  feet  of  air  are 
required,  making  18  pounds  of  gas  and  watery  vapor  after  com- 
bustion. 

For  burning  one  Ib.  of  olefiant  gas,  3.43  Ibs.  of  oxygen  are 
required,  making  4.43  Ibs.  of  carbonic  acid  and  water;  the 
volume  of  air  required  being  approximately  170  cubic  feet. 

157.  The  chemical  equivalent  of  a  substance,  in  chemistry,  is 
a  number  which  designates  the  proportions  by  weight  in  which 
that  substance  combines  chemically  with  others  ;   the  quantity 
of  that  substance  in  any  compound  being  either  in  simple  or 
multiple  proportion  of  its  chemical  equivalent. 

158.  The  atomic  formula  of  a  substance  designates  the  num- 
ber of  chemical   equivalents  of  the  substance  or  substances 
which  compose  it.     For  instance,  the  atomic  formula  of  hydro- 
gen being  H,  and  its  chemical  equivalent    being  1,  and  the 


78  COMBUSTION. 

atomic  formula  of  carbon  being  C,  and  its  chemical  equivalent 
being  6,  when  these  substances  unite  to  form  marsh-gas  the 
proportion  in  which  they  combine  is  known  to  be  C2  H4,  i.e., 
two  equivalents  by  weight  of  carbon  and  four  equivalents  of 
hydrogen,  or  6+6+1  +1+1+1  =  16.  So  that  the  atomic 
formula  of  marsh-gas  is  C2  H4,  and  its  chemical  equivalent 
16. 

159.  The  following  table  gives  the  atomic"  formulas,  the 
chemical  equivalents,  the  weight  of  oxygen,  and  the  weight 
of  the  products  of  combustion  in  oxygen  of  the  substances 
named,  the  atomic  formula  of  oxygen  being  O,  and  its  equiva- 
lent being  8 : 


TABLE  XVIII. 

Table  showing  the  atomic  formulas,  chemical  equivalents,  and  products  of 
combustion  in  pure  oxygen,  of  the  substances  named  in  the  first  column. 


Weight 

Weight 

Name  of  Com- 
bustible. 

Atomic 
Formula. 

Chemical 
Equiva- 
lent. 

Products  of 
Combustion. 

Atomic 
Formu- 
la. 

Chemi- 
cal 
Equiv- 
alent. 

Weight    of 
Fixed  Ox- 
ygen. 

of  Oxy- 
gen per 
Ib.  of 
Combus- 

of Pro- 
ducts of 
Combus- 
tion in. 

tible. 

Oxygen. 

Carbon...  .  . 

C 

6 

Carb.  Acid 

CO2 

22 

16 

2.66 

3.66 

Carbon  

C 

6 

Carb.  Ox.. 

CO 

14 

8 

1.33 

2.33 

Carb.  Oxide 

CO 

14 

Carb.  Acid 

CO2 

22 

8 

0.57 

1.57 

Hydrogen.  . 

H 

1 

Water  

HO 

9 

8 

8.00 

9.00 

Marsh-Gas.. 

C2  H4 

16 

Carb.  Acid 

SCO2 

44 

Water.  .... 

4HO 

64 

4.00 

5.00 

Olefiant  Gas 

C4  H4 

28 

Carb.  Acid 

4C02 

88 

Water  

4HO 

96 

3.43 

4.43 

160. ,  When  the  combustion  takes  place  in  air,  the  weight  of 
the  products  of  combustion  depend  on  the  quantity  of  air  re- 
quired in  each  case.  The  following  table  gives  a  recapitula- 
tion of  the  statements  already  made  in  general  terms  for  the 
combustion  of  1  Ib.  of  the  different  substances : 


COMBUSTION. 


TABLE    XIX. 

Table  showing  the  products  of  combustion  ofl  Ib.  of  the  substances  named,  in  air. 


Name  of 
Combustible. 

Products  of 
Combustion. 

Weight  of 
fixed  Oxy- 
gen in  Ibs. 

Weight  of 
the  Products 
of  Combus- 
tion in  Oxy- 
gen in  Ibs. 

Weight  of 
Air  Corre- 
sponding in 
Ibs. 

Weight  of 
Products  o£ 
Combustion 
in  Air  in  ibs. 

Carbon  

Carbonic  Acid 

2  66 

3  66 

11  29 

19  OQ 

Carbon           .    ... 

1  33 

2  33 

K    fiK 

6f»K 

Carbonic  Oxide  .  . 
Hydrogen  

Carbonic  Acid.  .  . 
Water 

0.57 
8  00 

1.57 
9  00 

2.42 
33  97 

3.42 

€>A    Q7 

Marsh-  Gas  

Carbonic  Acid  and 

Water 

4.00 

5  00 

16  99 

17  QQ 

Olefiant  Gas  

Carbonic  Acid  and 
Water  

3.43 

4.43 

1457 

15  57 

161.  Most  of  the  substances  involved  in  ordinary  combustion 
are  found  only  in  the  gaseous  state,  and  at  the  moment  of  com- 
bination it  is  supposed  that  all,  even  carbon,  becomes  gaseous. 
It  is  hence  convenient  and  often  necessary  to  know  the  pro- 
portions ~by  volume  in  which  combinations  take  place. 

162.  It  is  a  general  principle  of  chemistry  that  perfect  gases, 
at  a  given  pressure  and  temperature,  combine  in  simple  numeri- 
cal proportions  by  volume :  the  chemical  equivalents  being  pro- 
portional to  the  densities  or  multiples  of  the  densities. 

The  following  table  exhibits  the  products  of  combustion  by 
volume  of  one  volume  (1  cubic  foot)  of  each  of  the  combusti- 
bles named,  and  also  in  exact  figures  the  number  of  cubic  feet 
of  air  necessary  to  burn  1  Ib.  of  each  of  the  substances  to  form 
the  products  specified  : 

TABLE  XX. 

Table  of  the  products  of  combustion  by  volume  of  one  volume  of  the  various 
combustibles  named. 


Total 

Volume  1 

Name  of  Com- 
bustible. 

Composi- 
tion by 
Volume  of 
one  Vol- 
ume. 

Products  of 
Combustion. 

Composition 
by  Volume 
of  Products 
of  Combus- 
tion. 

Volume 
of  Pro- 
ducts of 
Combus- 
tion in 
Air. 

of  Air  re- 
quired to 
burn  1 
Ib.  of 
Comb., 
in  cu.  ft. 

Volume 
of  Air 
Corre- 
spond- 
ing. 

Volume 
of  fixed 
Oxygen. 

Volume 
of  the 
Pro- 
ducts of 
Combus- 
tion. 

Carbon  

C 

Carb.  Acid. 

2(^C+O) 

137.50 

137.50 

9.39 

2.0 

2 

Carbon  

C 

Carb.  Ox.  . 

2(iC  +  iO) 

83.28 

68.66 

4.69 

1.0 

2 

Carb.  Oxide 

iC  +  |0 

Carb.  Acid. 

l(iC  +  0) 

36.14 

29.80 

2.35 

0.5 

1 

Hydrogen.. 

H 

Water  .... 

l(H-HO) 

509.1 

419.7 

2.35 

0.5 

1 

Marsh  -Gas. 

iC  +  2H 

Carb.  Acid. 

1(J,C  +  O) 

Water  

2(H  +  J,0) 

228.3 

206.4 

9.39 

2.0 

3 

Olefiant  Gas 

C  +  2H 

Carb.  Acid. 

2(iC  +  0) 

Water  

2(H  +  -'0) 

188.5 

176.6 

14.08 

3.0 

4 

80  COMBUSTION. 

The  last  column  shows  the  total  volume  of  the  gaseous  pro- 
ducts of  combustion  in  air.  The  numbers  in  this  column  are 
found  in  the  following  manner:  For  the  combustion  to  form 
carbonic  acid  2  cubic  feet  of  oxygen  combine  writh  1  cubic 
foot  of  carbon  to  form  2  cubic  feet  of  carbonic  acid.  The 
volume  of  the  carbonic  acid  after  the  combustion  will  be  the 
same  as  the  volume  of  the  fixed  oxygen,  and  after  the  combus- 
tion, the  volume  of  the  products  remains  the  same  as  the  vol- 
ume of  air  required  for  combustion. 

In  the  combustion  of  carbon  to  form  carbonic  oxide,  however, 
it  will  be  observed  that  for  each  cubic  foot  of  oxygen  used,  two 
cubic  feet  of  carbonic  oxide  are  produced.  The  amount  of  air 
necessary  to  burn  1  Ib.  of  carbon  to  form  carbonic  oxide  is  given 

/*  o  />  /"» 

in  the  table  68.66  cubic  feet,  which  contains  T-QT  —  14.62  cubic 


feet  of  oxygen.  Each  cubic  foot  of  oxygen  with  the  carbon 
forms  two  cubic  feet  of  carbonic  oxide  ;  so  that  if  we  add  one 
cubic  foot  for  each  cubic  foot  of  oxygen  to  the  amount  of  air 
required  (68.66  cubic  feet),  we  shall  obtain  the  total  gaseous 
product,  83.28  cubic  feet. 

In  the  combustion  of  hydrogen  the  same  ratio  is  observed. 
In  the  combustion  of  marsh-gas  one  cubic  foot  is  to  be  added 
for  every  two  cubic  feet  of  oxygen  ;  and  for  olefiant  gas,  one 
cubic  foot  for  every  three  cubic  feet  of  oxygen. 

These  tables  are  valuable  in  determining  the  quantity  of  gas 
that  is  discharged  from  furnaces,  and  also  in  the  discussion  of 
problems  relating  to  draft,  and  the  quantity  of  heat  transferred 
to  water  in  the  generation  of  steam. 

In  regard  to  the  vapor  of  water,  if  it  be  cooled  to  the  point 
of  condensation,  its  volume  will  practically  disappear  from  the 
volume  of  products  of  combustion,  causing  a  considerable  re- 
duction of  volume  in  the  case  of  the  hydro-carbons,  and  making 
the  volume  of  the  gaseous  products  even  less  than  that  of  the 
air  introduced. 

163.  Heat  Evolved  in  Chemical  Combination.  —  An  im- 

portant consequence  of  the  dynamic  law  of  heat,  and  one  which 
has  been  experimentally  verified,  is,  that  all  chemical  changes 
are  accompanied  by  corresponding  changes  of  heat.  Chemical 
action  and  heat  are  mutually  convertible  ;  and  although  the 
quantity  of  heat  evolved,  or  annihilated,  in  any  chemical  change 


COMBUSTION.  81 

can  only  be  experimentally  determined,  yet  it  has  been  estab- 
lished that  the  combination  of  any  two  bodies,  chemically,  is 
attended  by  the  evolution  of  a  quantity  of  heat  equal  to  that 
which  disappears  in  their  separation. 

164  The  quantities  of  heat  evolved  or  disengaged  in  chemical 
combinations  are  found  experimentally  by  means  of  calorime- 
ters. These  measurers  of  heat  are  employed  in  various  forms, 
and  operate,  generally,  in  such  a  manner  as  to  exhibit  the 
effects  of  the  heat  evolved  in  acting  on  a  given  substance,  such 
as  the  melting  of  ice  or  the  raising  of  the  temperature  of  a 
given  quantity  of  water  ;  the  quantities  of  heat  being  thus  in- 
directly measured  by  being  transferred  to  some  body  in  which 
these  effects  can  be  estimated  in  units  of  heat. 

The  following  table  gives,  in  English  units,  the  quantities  of 
heat  disengaged  by  the  combustion  of  the  bodies  named,  by 
oxygen : 


TABLE  XXI. 

Heat  evolved  by  the 

Names  of  Combustibles.  combustion  of  1  Ib.  Names  of  Observers, 

of  combustible. 

Hydrogen 62.000  Favre  arid  Silberman. 

Carbon 14.544  " 

Graphite 14.035  " 

Native  Sulphur 3.966 

Carbon  to  Carbonic  Oxide 4.466 

Carbonic  Oxide  to  Carbonic  Acid.         4.325  " 

Marsh-Gas 23.513  " 

OlefiantGas 21.344  " 

Turpentine 19.533  " 

Alcohol 12.931  " 

Ether 16.250  " 

Spermaceti 18.616 

Anthracite  of  Pennsylvania 14.114  (calculated).     Morin  and  Tresca. 

u          of  Mayenne 15.689 

Bituminous  Coals  (mean) 14.400 

Lignites  (mean) 12.240 

Peat 9.000 

Peat,  20  per  cent,  water  7.200 

Coke 12.600 

Dry  Wood 7.200 

Wood  containing  20  water 5.600 

Ordinary  Illuminating  Gas 18. 000 

Gas  from  Iron-furnaces 1.620 

Petroleum 21.000 

In  this  manner  the  heat  evolved  in  the  combination  of  both 
simple  and  compound  bodies  has  been  determined  by  many  ob- 


82  COMBUSTION. 

servers,  especial  authority  being  given  to  those  of  Favre  and 
Silberman.  In  the  chemical  changes  which  compound  bodies 
undergo,  it  may  be  stated,  as  a  general  law,  that  the  heat  which 
appears  or  disappears  is  the  resultant  of  the  action  of  the  simple 
elements,  and  where  a  compound  consists  of  combustible  ele- 
ments only,  like  carbon,  and  hydrogen,  the  heat  disengaged  is 
the  sum  of  the  quantities  of  heat  disengaged  l>y  the  combus- 
tion of  the  elements  separately. 

This  law,  though  not  indisputably  established,  is  considered 
sufficiently  exact  for  all  ordinary  purposes. 

The  temperature  at  which  bodies  combine,  although  affecting 
the  rapidity  or  energy  of  chemical  action,  does  not  affect  the 
total  quantities  of  heat  involved  in  the  change. 


CHAPTER  III. 

FUEL. 

165.  FROM  the  preceding  chapter  it  appears  that  combustibles 
employed  for  the  purpose  of  generating  heat  may  be  used  in 
all  three  states  of  aggregation,  solid,  liquid,  and  gaseous,  and 
that  the  heat  disengaged  in  the  combustion  of  one  pound  of  com- 
bustible is  greater  for  some  gases  and  liquids  than  for  any  solid 
combustible. 

166.  The  question  of  utility,  or  value,  of  a  combustible,  de- 
pends, however,  largely  on  other  considerations  than  its  heat- 
producing  power.     The  only  liquid  that  is  found  in  abundance 
in  nature,  which  might  be  employed  as  a  fuel,  is  petroleum, 
and  the  cost  of  this  liquid,  combined  with  characteristics  which 
make  it  difficult  and  unsafe  for  transportation  in  large  quanti- 
ties as  fuel,  renders  it  unfit  and  unprofitable  in  most  cases,  ex- 
cept for  producing  light.    It  is  only  in  exceptional  circumstances 
that  it  is  employed  in  the  generation  of  steam.    Its  chemical 
composition  is,  according  to  Tate,  nearly  identical  with  that 
of  oil  of  turpentine,  viz. :  equal  equivalents  of  carbon  and  hy- 
drogen, and  its  calorific  power  estimated  to  be  21,000  English 
units. 

For  transportation  safely  in  large  quantities  air-tight  metallic 
vessels  are  necessary.  It  gives  off,  at  ordinary  temperatures, 
vapors,  which,  if  they  become  mixed  with  air  in  suitable  propor- 
tions in  enclosed  spaces,  form  a  dangerous  explosive  mixture. 
Atmospheric  air  mechanically  charged  with  the  liquid  hydro- 
carbons is  employed  to  some  extent  both  for  heating  and  light- 
ing purposes.  The  heating  power  of  such  a  saturated  air  is 
considered  to  be  about  the  same  as  that  of  illuminating  gas.  A 
peculiar  property  of  this  mixture  is  that  a  portion,  at  least,  if 
not  all,  of  the  oxygen  necessary  for  combustion  is  contained  in 
the  mixture.  The  liquid  hydro-carbons,  as  is  well  known,  may 
be  produced  by  the  distillation  of  the  bituminous  coals. 

167.  Combustible   gases    are  also   found  in   some  localities 


84  .  FUEL. 

under  such  conditions  that  they  are  collected  and  burned  di- 
rectly from  their  natural  reservoirs ;  but  for  universal  use  they 
are  produced  by  distillation  of  the  coals. 

Ordinary  illuminating  gas  is  not  only  employed  for  light- 
ing, but  for  heating  purposes,  and  is  also,  to  some  extent, 
burned  directly  in  the  cylinders  of  engines  to  furnish  motive 
power.  Its  composition  varies  with  the  kind  and  quality  of 
coal  used  in  distillation.  A  mean  or  average  composition  from  the 
French  coals  is  given  by  Morin  and  Tresca,  as  follows,  reduced 
to  English  units : 

TABLE  XXII. 

One  cubic  foot  Weight  of  one  Weight  of  each  in        Weight  of  each 

contains  of  cubic  foot  in  pounds.  one  cubic  foot.  in  one  pound. 

Marsh-gas 0.59  0.0454  0.0268  0.612 

Olefiant  gas 0.09  0.0795  0.0072  0.164 

Carbonic  oxide....   0.07  0.0788  0.0055  0.126 

Hydrogen 0.21  0.0056  0.0012  0.027 

Nitrogen 0.04  0,0786  0.0031  0.071 


1.00  0.0438  1.000 

From  the  above  table  it  appears  that  the  weight  of  one  cubic 
foot  of  illuminating  gas  is  0.0438  pounds,  and  the  volume  of  one 
pound  ¥¥V?rj  O1>  22.83  cubic  feet,  at  the  temperature  and  pres- 
sure at  which  the  standard  volumes  are  estimated.  All  the 
gases,  except  nitrogen,  which  enter  into  the  composition  of  this 
illuminating  gas  are  combustible. 

The  table  on  page  85,  also  from  Morin  and  Tresca' s  work,  gives 
the  products  of  combustion  of  illuminating  gas  in  English  mea- 
sures, and  also  the  volumes  of  air  necessary  to  burn  one  cubic 
foot. 

In  the  combustion  of  illuminating  gas  the  volume  of  the  pro- 
ducts of  combustion  is  essentially  the  sum  of  the  primitive  vol- 
umes of  the  air  necessary  for  combustion,  and  the  volume  of  the 
gas;  for  example,  1  cubic  foot  of  gas  requires  7.462  cubic  feet 
of  air,  and  the  volume  of  the  products  is  8.462  cubic  feet. 

In  cases  where  the  vapor  of  water  and  carbonic  acid,  or 
either  of  these  products,  is  condensed  to  the  liquid  form,  there 
will  be  a  considerable  reduction  in  volume.  For  watery  vapor 
this  condensation  may  easily  be  effected  by  cooling;  and  for 
the  carbonic  acid,  by  the  absorption  of  the  acid  by  alkaline  solu- 
tions. If  the  vapor  of  water  alone  is  condensed,  the  reduc- 
tion of  volume  of  the  products  will  be  about  two-tenths  ;  if  both 


FUEL. 


85 


the  carbonic  acid  and  the  water  are  condensed,  the  reduction  of 
volume  will  be  three-tenths ;  the  combustion  in  both  cases  be- 
ing; in  air. 

O 

The  gases  which  are  evolved  when  bituminous  coal,  wood,  or 
peat  is  heated,  are  composed  of  carbonic  oxide  and  hydro-car- 
bons ;  these  gases  are  produced  in  all  furnaces  in  which  these 
combustibles  are  employed,  and  the  supply  of  air  and  the  man- 
agement of  the  furnaces  should  be  such  as  to  completely  burn 
the  gaseous  products ;  otherwise  they  may  pass  through  the 
chimney  unconsumed,  involving  not  only  a  loss  of  heat,  but 
producing  srnoke  and  soot. 

TABLE  XXIII. 

Combustion  of  Illuminating  Gas. 


Composition  of  one 
cubic  foot  of  the 

gas. 

Products    of      com- 
bustion. 

Volume 
of     car- 
bonic 
acid. 

Volume 
of  water 

Volume 
of  nitro- 
gen. 

Total 
volume 
of  pro- 
ducts. 

Volume 
of   fixed 
oxygen. 

Volume 
of    air 
correspond- 
ing. 

Marsh  -gas. 
0.59 

Carbonic    acid. 
0.59  (iO  +O) 
Water. 
0.59x2(H  +  iO) 

0.59 

1.18 

0.59 

1.18 

0.59 
0.59 

2.769 
2.769 

Olefiant  gas. 
0.09 

Carbonic  acid. 
0.09x2  (iO  +  O) 
Water. 
0.09x2(H  +  iO 

0.18 

0.18 

0.18 
0.18 

0.18 
0.09 

0.845 
0.422 

Carbonic  oxide. 
0.07 

Carbonic  acid. 
0.07  (iC  +  O) 

0.07 

0.07 

0.035 

0.164 

Hydrogen. 
0.21 

Water. 
0.21    (H  +  iO) 

0.21 

0.21 

0.015 

0.493 

Nitrogen. 
0.07 

Nitrogen. 
0.04N. 

0.04 

0.04 

1.00  cubic  foot. 

0.84 

1.57 

0.04 

2.45 

1.59 

7.462 

168.  Natural  Solid  Combustibles  may  be  arranged  under 
the  following  designations  : 

Anthracite  Coal. 
Bituminous  Coal. 


lc  •>  « 


86  FUEL. 

A  classification  which  represents,  generally,  the  geological  oc- 
currence of  the  vegetation  from  which  the  fuel  has  been  pro- 
duced. 

169.  Charcoal  and  Coke  are  to  some  extent  artificial  combus- 
tibles, the  former  being  produced  by  the  carbonization  of  wood 
or  peat,  and  the  latter  by  the  carbonization  of  bituminous  coal. 
In  both  cases  the  volatile  matters  of  the  wood  or  coal  are  driven 
off  by  heat,  leaving  a  residuum  which  is  composed  principally  of 
carbon  and  fixed  inorganic  matters. 

170.  Artificial  Solid  Combustibles  composed  of  coal-dust, 
used  taiibark,  and  other  refuse  combustible  matters,  are  made  to 
a  considerable  extent  in  France  and  other  parts  of  Europe,  in 
order  to  utilize  what  would  otherwise  be  wasted  materials.    The 
dust  or  other  refuse  matter  is  mixed  with  a  small  quantity  of 
clay,  and  sometimes  a  small  quantity  of  bituminous,  matter  is 
added  to  facilitate  combustion.     The  mixture,  compressed  into 
the  form  of  bricks,  has  the  property  of  burning  slowly  without 
being   easily  extinguished,  and  giving  out  a  regular  and  con- 
tinuous heat. 

Large  establishments  in  France,  Belgium,  and  Germany  are 
devoted  to  the  manufacture  of  these  artificial  combustibles, 
the  bricks  being  formed  under  powerful  hydraulic  pressure 
where  the  combustible  is  designed  for  portable  engines,  though 
often  submitted  to  the  natural  drying  action  of  the  air,  where 
the  fuel  is  intended  for  domestic  use. 

Morin  and  Tresca  give  the  following  composition  for  some 
of  these  artificial  combustibles,  viz. :  80  to  85  per  cent,  of  carbon, 

4  to  5  of  hydrogen,  about  5  per  cent,  of  volatile  products,  and 

5  to  8  per  cent,  of  ashes. 

171.  Properties  of  Anthracite. — This  combustible    stands 
first  in  value,  at  least  in  this  country,  as  a  fuel,  containing  as  it 
does  the  largest  proportion  of  pure  carbon,  the  element  on  which 
the  industrial  and  commercial  values  of  a  given  fuel  most  depend. 

The  American  anthracites  are  not  generally  subject  to  the 
objection  found  to  the  use  of  the  English  and  French  antlira- 
.cites,  of  decrepitating,  or  breaking  up  into  small  fragments, 
during  combustion,  and  are  therefore  available  for  nearly  all 
purposes  in  the  generation  of  heat,  whether  in  domestic  use,  the 
generation  of  steam,  or  in  metallurgical  operations. 

This  combustible  is  not  easily  ignited,  and  is  readily  extin- 
guished if  the  supply  of  air  is  not  kept  up,  rendering  the 


FUEL.  87 

management  of  the  combustion  difficult.  It  is  not  easily  broken, 
and  may  therefore  be  transported  without  great  loss  from  the 
accumulation  of  dust. 

172.  Bituminous  Coals. — The  bituminous  coals  are  most 
universally  distributed,  and  constitute  the  real  basis  of  indus- 
trial enterprise  and  progress. 

The  varieties  of  coal  in  this  class  are  so  great  that  it  is 
difficult  to  establish  a  distinction  between  some  of  the  semi- 
bituminous  coals  and  anthracite  on  one  side,  and  bituminous 
coals  and  the  lignites  on  the  other.  The  bituminous  coals  are 
distinguished  by  the  presence  of  more  or  less  volatile  matters 
(hydro-carbons)  which  are  given  off  on  the  application  of  heat. 
In  ordinary  combustion  in  air,  these  volatile  matters  form  a 
large  volume  of  combustible  gas  above  the  fuel  during  the  first 
stages  of  the  combustion,  which  constitutes  a  considerable  part 
of  the  fuel,  and  usually  burns  with  considerable  flame.  If  the 
combustion  of  these  gaseous  matters  is  not  complete,  particles  of 
pure  carbon  are  set  free  and  form  smoke  or  soot. 

The  prevention  of  smoke  from  bituminous  coal  has  always 
been  found  a  difficult  problem ;  a  sufficient  supply  of  ail- 
properly  mingled  with  the  gases,  and  a  high  temperature  at  the 
same  time,  for  ignition  and  combustion,  are  the  elements  which 
must  be  combined  to  make  the  combustion  complete. 

The  bituminous  coals  of  England  are  divided  into  calling  and 
non-caking  coals,  which  correspond  to  the  American  designa- 
tions caking  and  free-burning  coals.  The  free-burning  or  non- 
caking  coals  are  those  in  which  the  lumps  or  pieces  retain  to  a 
great  extent  their  original  forms,  leaving  the  interspaces  free 
for  the  circulation  of  air.  The  caking  coals  are  those  which, 
during  combustion,  assume  to  a  certain  extent  a  pasty,  glutinous 
form,  the  lumps  sticking  together  in  such  a  manner  as  to 
prevent  the  circulation  of  air  in  the  mass.  This  property  is 
valuable  in  some  metallurgical  operations  where  air  is  supplied 
to  the  interior  of  the  fire  by  a  powerful  blast ;  but  in  others, 
especially  in  the  generation  of  steam,  where  it  is  important  to 
utilize  as  much  as  possible  the  external  radiant  heat  of  the  fire, 
and  where  a  free  circulation  of  air  throughout  the  mass  is  indis- 
pensable, the  caking  coals  are  objectionable. 

In  both  anthracite  and  bituminous  coals,  inorganic  substances 
occur,  which  often  modify  greatly  their  value.  This  inorganic 
matter  is  derived  in  part  from  the  vegetable  tissues  from  which* 


88  FUEL. 

the  coal  is  produced,  but  largely  also  from  the  earthy  matters 
in  the  strata  deposited  with  the  coal.  The  admixture  of  seams 
of  slate  or  shale  in  lumps  of  -coal  is  not  uncommon ;  but  such 
imperfections  can  generally  be  detected  by  superficial  observa- 
tion. The  quantity  of  ashes  is  generally  the  only  evidence  of 
the  amount  of  inorganic  matter,  and  to  some  extent  is  an  index 
of  the  value  of  the  coal.  The  proportion  of  ashes  may  be  so 
great  as  materially  to  impair  the  quality  of  the  coal.  From  one 
to  four  per  cent,  of  ashes  is  the  ordinary  amount  in  the  best 
coals,  though  in  some  valuable  coals  the  proportion  of  ashes  is 
much  larger,  amounting  in  some  instances  to  over  ten  per  cent. 
The  ashes  are  often  of  such  a  nature  that  they  fuse  or  melt,  and 
form  masses  of  clinker;  and  when  this  takes  place  to  any 
considerable  extent,  the  coal  is  inferior  for  use  in  steam-boilers. 
The  clinker,  if  not  repeatedly  removed,  impairs  the  circulation 
of  air,  and  may  adhere  to  the  grate-bars,  thus  causing  their 
destruction.  The  presence  of  earthy  matters  in  connection  with 
clinker  is  still  more  injurious. 

Nearly  all  bituminous  coal  contains  iron  pyrites,  the  oxidation 
of  which  may  produce  spontaneous  combustion  ;  and  when  this 
substance  exists  in  considerable  quantities  in  coal,  especial 
watchfulness  is  necessary  when  the  coal  is  stored  in  confined 
places,  such  as  the  coal-bunkers  on  steamships.  Iron  pyrites 
also  assists  the  fusion  of  the  ashes  and  the  formation  of  clinker. 
Bituminous  coal  usually  contains  65  to  85  per  cent,  of  carbon, 
about  6  per  cent,  of  hydrogen,  5  to  6  per  cent,  of  volatile  mat- 
ters, and  3  to  6  per  cent,  of  inorganic  matter. 

173.  Lignites. — The  lignites,  which  approach  in  composition 
and  geological  age  the  bituminous  coals,  differ  from  them  only  in 
degree,  being  generally  inferior,  though  often  fit  for  use  as  fuel. 
The  more  recent  lignites,  which  preserve  the  structure  of  the 
vegetable  tissues,  are  seldom  used.  Where  other  fuel  is  scarce 
these  lignites  may  take  the  place  of  wood,  being  intermediate 
in  properties  and  value  between  wood  and  coal.  They  generally 
contain  a  large  amount  of  water. 

1Y4:.  Peat. — This  combustible  differs  from  lignite  in  present- 
ing a  peculiar  spongy  appearance,  resulting  from  the  vegetable 
tissues  from  which  it  is  produced.  It  is  apparently  composed  of 
the  debris  of  plants- and  grasses  which  have  grown  during  the 
present  geological  epoch  upon  the  sites  of  what  are  now  recog- 
nized as  peat-beds.  It  contains  a  large  amount  of  water,  and  is 


FUEL.  89 

usually  prepared  by  drying  in  the  sun  and  open  air.  Used  in 
this  state,  which  involves  little  expense  in  preparation,  it  may  be 
obtained  at  so  low  a  price  as  to  make  it  profitable  as  a  fuel,  even 
on  railways.  It  is  composed,  according  to  the  determinations  of 
Regnanlt,  whose  analyses  for  other  combustibles  have  been  ap- 
proximately given  above,  of  about  60  per  cent,  of  carbon,  5  per 
cent,  of  hydrogen,  about  30  per  cent,  of  oxygen  and  nitrogen, 
and  5  to  8  per  cent,  inorganic  matter.  Its  calorific  power,  in  pro- 
portion to  its  bulk  in  the  crude  state,  is  small,  and  many  attempts 
have  been  made  to  condense  it  by  mechanical  pressure.  In 
Germany  this  combustible  is  employed  to  a  considerable  extent 
for  locomotives,  in  both  the  crude  and  compressed  states.  Char- 
coal from  peat  is  employed  in  metallurgical  operations,  but  is 
too  costly  for  ordinary  purposes  in  the  generation  of  steam. 

175.  Wood. — In  localities  where  the  removal  of  the  primitive 
forests  is  the  first  necessary  step  to  the  cultivation  of  land,  the 
use  of  wood  for  the  generation  of  steam  for  manufacturing  pur- 
poses, and  for  the  purposes  of  transportation,  is  economical ;  and 
in  such  localities  it  is  the  principal  source  of  fuel.  But  the 
secondary  growth  of  forest-trees,  as  countries  become  settled,  is 
too  much  needed  for  necessary  domestic  uses,  and  for  timber, 
to  be  employed  extensively  in  the  production  of  steam.  The 
exceptions  to  this  general  rule  are  those  cases  where  the  refuse 
pieces  of  timber,  sawdust,  and  shavings  which  accumulate  in 
manufacturing  establishments,  are  thus  utilized  as  fuel. 

The  value  of  'wood  as  a  fuel  depends  greatly  on  its  dryness. 
According  to  the  analysis  of  M.  Baer,  given  by  Morin  and  Tres- 
ca,  all  the  common  woods,  whether  hard  or  soft,  have  nearly  the 
same  general  composition,  containing  about  50  per  cent,  of 
carbon,  6  per  cent,  of  hydrogen,  43  to  45  of  oxygen,  and  less 
than  1  per  cent,  of  ashes. 

The  proportion  of  oxygen  by  weight  is,  according  to  this  anal- 
ysis, about  seven  times  that  of  the  hydrogen,  or  nearly  sufficient 
for  the  combustion  of  all  the  hydrogen  present ;  so  that  it  may 
be  said  that  all  wood  contains  about  50  per  cent,  of  carbon  and 
about  1  per  cent,  of  free  hydrogen. 

Wood  contains  also,  mechanically,  a  large  proportion  of  water. 
After  two  years  of  natural  ;< seasoning"  it  is  found  to  contain 
about  20  per  cent.,  and  sometimes  30  per  cent.,  of  water,  the  effi- 
cacy of  the  seasoning  depending  on  the  condition  of  the  wood, 
whether  split,  sawed,  or  left  in  the  round  state  in  which  it  grows. 


90  FUEL. 

When  subjected  to  distillation  or  heating,  by  which  the  volatile 
matters  are  driven  off,  the  products  are  a  residue  of  about  15 
per  cent,  of  carbon,  85  of  volatile  matters,  hydro-carbons,  and 
other  gaseous  products,  and  less  than  -J  per  cent,  of  ashes. 

In  employing  wood  for  heating  purposes  it  is  important,  there- 
fore, as  in  the  case  of  bituminous  coal,  to  provide  for  the  com- 
bustion of  the  escaping  gases. 

The  calorific  power  of  dry  wood  is  about  7,200  English  units 
of  heat  for  the  combustion  of  1  lb.,  and  for  wood  containing  20 
per  cent,  of  water,  6,400  units  of  heat. 

176.  Wood-Charcoal. — This  combustible  is  produced  by  the 
heating  of  wood,  without  access  of  air,  until  the  volatile  matters 
are  driven  off  and  a  residue  of  carbon  and  a  small  quantity  of 
volatile  matter  remains.  The  lowest  temperature  at  which  this 
occurs  is  about  400°  Fahr.,  but  a  red-heat  is  indispensable  for 
complete  carbonization. 

The  volatile  matters  driven  off  consist  of  water,  acetic  acid, 
tar,  and  other  condensable  matters,  and  the  permanent  gases,  car- 
bonic acid,  carbonic  oxide,  hydrogen,  and  carburetted  hydrogen. 

The  quality  of  the  charcoal  varies  to  some  extent  with  the 
temperature  of  carbonization.  It  is  stated  by  Percy  that  char- 
coal made  at  about  260°  C.  burns  most  easily,  but  that  made  at 
1,000°  and  1,500°  C.  cannot  be  ignited  like  ordinary  charcoal. 

"  Charcoal,  made  at  a  constant  temperature  of  300°  C.,  takes 
fire  in  air  when  heated  to  360°  and  380"'  C.  Charcoal  made  be- 
tween 260°  and  280°  C.  ignites  between  340°  C.  and  360°  C. 
That  made  between  290°  C.  and  350°  C.  ignites  between  360° 
C.  and  370°  C.  That  made  at  432°  C.  burns  at  about  400°  C., 
and  that  made  between  1,000°  C.  and  1,500°  C.  burns  between 
600°  and  800°  C."  * 

The  composition  of  charcoal  varies  somewhat  with  the  wood 
from  which  it  is  produced,  and  especially  with  the  temperature 
of  carbonization  ;  but  of  the  ordinary  kinds  the  composition 
given  by  various  analyses  is  approximately  as  follows  : 

Water 6     to    8  per  cent. 

Carbon 85     to  89          " 

Hydrogen 2     to    3          " 

Oxygen 1     to    3          " 

Ashes 1.5  to    3          " 

*  Percy's  Metallurgy. 


FUEL.  91 

The  higher  the  temperature  of  carbonization  the  greater  will 
be  the  proportion  of  pure  carbon,  and  the  less  the  proportion 
of  oxygen,  hydrogen,  and  nitrogen. 

Charcoal  absorbs  water  rapidly,  the  commercial  charcoal 
generally  containing  10  to  12  per  cent,  of  moisture.  In  the  state 
of  powder  this  absorption  is  increased,  and  it  is  less  for  charcoals 
produced  at  higher  temperatures  than  for  low  temperatures. 

It  is  evident  from  the  above  that  charcoal  must  be  an  expen- 
sive fuel  for  the  purposes  of  generating  steam,  because  a  large 
part  of  the  combustible  matter  of  the  wood  is  driven  off,  and, 
unless  utilized,  is  wasted.  The  cost  of  this  combustible  is  thus 
an  objection  to  its  general  use  for  generating  steam,  except  in 
exceptional  cases. 

177.  Coke  is  obtained  from  the  distillation  of  bituminous 
,  coal  by  processes  analogous  to  those  employed  in  the  preparation 
of  charcoal ;  the  quality  of  the  coke  depending  greatly  on  the 
coals  from  which  it  is  derived,  and  also  on  the  process  of 
coking.  Ordinary  coke  contains  about  90  per  cent,  of  carbon, 
6  per  cent,  of  ash,  and  3  to  4  per  cent,  of  oxygen,  hydrogen, 
and  nitrogen.  It  absorbs  water  rapidly,  and  hence  should  not 
be  left  exposed  to  the  weather.  Immersed  in  water,  it  may  ab- 
sorb as  much  as  30  to  50  per  cent,  of  its  weight  of  water.  Be- 
fore being  burnt,  therefore,  it  should  be  dried  by  exposure  in 
dry  air,  if  it  has  been  long  subjected  to  conditions  favorable  to 
the  absorption  of  moisture. 

Coke  was  formerly  almost  exclusively  used  in  France,  and 
England  for  locomotives,  principally  on  account  of  its  intrinsic 
value  as  a  fuel,  as  it  makes  a  steady,  constant  fire,  and  burns 
without  smoke. 

Gas-cokes,  which  are  extensively  used  in  cities  for  domestic 
fuel,  contain  less  carbon,  and  more  of  inorganic  matter  pro- 
ducing ashes,  than  the  cokes  prepared  for  locomotives  and  for 
metallurgical  operations ;  the  composition  of  gas-coke,  accord- 
ing to  Morin  and  Tresca,  being  about  60  per  cent,  of  carbon, 
8  to  20  of  hydrogen,  and  20  to  30  of  ashes. 

The  use  of  coke  as  a  fuel  for  the  generation  of  steam  is,  as  in 
the  case  of  charcoal,  restricted  by  its  cost.  It  is  only  where 
the  volatile  products  of  the  distillation  are  utilized,  as  in  the 
manufacture  of  illuminating  gas,  that  the  residual  coke  can  be 
sold  at  a  price  which  renders  it  advantageous  for  the  generation 
of  steam. 


92  FUEL. 

178.  The  kind  or  quality  of  fuel  to  be  employed  in  the  gene- 
ration of  steam  for  industrial  or  commercial  purposes,  is  often 
determined  by  local  or  other  conditions,  independent  of  the 
special  characteristics  of  the  fuel.  In  nearly  all  cases  the  ele- 
ment of  cost  is  the  controlling  one,  account  being  taken  of  all 
the  conditions  essential  to  economy.  Where  the  question  of 
choice  of  fuel  for  a  special  purpose  is  to  be  decided,  all  these 
conditions  are  to  be  considered  in  connection  with  the  quality 
of  the  fuel. 

Professor  Walter  N".  Johnson,  in  his  report  to  the  Navy  De- 
partment, in  1844,  on  "American  coals  applicable  to  steam  navi- 
gation and  to  other  .purposes,"  establishes  ten  "ranks,"  as  fol- 
lows. Names  of  coals  arranged  in  the  order  of 

1.  Their  relative  weights. 

2.  Rapidity  of  ignition. 

3.  Completeness  of  combustion. 

4.  Evaporative  power  under  equal  weights. 

5.  Evaporative  power  under  equal  bulks. 

6.  Evaporative  power  of  combustible  matter. 

7.  Freedom  from  waste  in  burning. 

8.  Freedom  from  tendency  to  form  clinker. 

9.  Maximum  evaporative  power  under  equal  bulks. 
10.  Maximum  rapidity  of  combustion. 

It  was  found  impossible  to  select  any  one  coal  which  could 
be  considered  first  in  all  these  qualities ;  and  it  is  not  even  pos- 
sible to  attach  equal  importance  to  all  the  ranks.  For  different 
purposes  the  relative  values  of  the  different  qualities  must  be 
differently  estimated. 

For  the  purposes  of  steam  navigation  he  attaches  the  most 
importance  to  the  fifth  rank,  "the  evaporative  power  under 
equal  bulks,"  because  stowage-room  occupied  by  the  fuel  is  an 
important  feature  in  steam  navigation. 

With  the  fifth  rank  he  combines  the  eighth  and  tenth,  viz., 
^freedom  from  clinker"  and  " maximum  rapidity  of  action." 
According  to  this  report  the  American  coals  are  generally 
superior  to,  or  at  least  not  surpassed  by,  the  foreign  coals,  in  all 
the  most  desirable  qualities  for  producing  steam. 

In  regard  to  the  use  of  coke,  peat  dried  in  the  open  air,  and 
wood,  it  is  stated  by  Peclet  that  experiments  made  in  Austria 


FUEL. 


93 


demonstrated  that  one  pound  of  coke  is  equivalent  to  2.25 
pounds  of  peat,  and  to  about  0.11  of  a  cubic  foot  of  pine  or 
0.09  of  a  cubic  foot  of  oak  wood. 

179.  The  following  useful  table  is  taken  from  the  work  of 
Mori  11  and  Tresca,  the  quantities  being  converted  from  French 
to  English  units.  It  gives  the  constitution,  calorific  power, 
quantity  of  air  necessary  for  combustion,  and  volume  of  the  pro- 
ducts of  combustion,  for  the  various  combustibles  employed  in 
industrial  operations,  the  quantities  being  average  or  mean 
values  for  the  combustibles  employed  in  Europe. 


TABLE  XXIV. 

Table  showing  the  composition  and  calorific  power  of  various  combustibles, 
the  quantity  of  oxygen  and  air  necessary  for  combustion,  and  the  volume 
of  the  products  of  combustion  ofl  Ib.  of  combustible. 


Name  of  Combusti- 
ble. 

Composition. 

Calorific 
Power. 

Weight  of 
Oxygen 
necessary 
for-  Com- 
bustion. 

Weight 
of  Air 
necessa- 
ry for 
Combus- 
tion. 

Volume 
of  Air  cor- 
respond- 
ing, 
cu.  feet. 

Volume 
of  Pro- 
ducts, 
cu.  feet. 

C. 

H. 

Volatile 
Matter. 

Ashes. 

Carbon  !1.00 

14,400 
13,500 
14,400 
11,700 
9,000 
7,200 
12,600 
9,000 
7,200 
5.400 
10,800 
52,200 
4,320 
18,000 

1,620 

2.66 
2.64 
2.66 
2.26 
1.86 
1.49 
2.26 
2.18 
1.75 
1.40 
1.86 
8.00 
0.57 
2.64 

0.23 

11.29 
11.21 
11.29 
9.69 
7.90 
6.32 
9.69 
9.25 
7.43 
5.94 
7.90 
33.97 
2.42 
11.22 

0.99 

137.6 
138.9 
139.6 
120.2 
97.9 
78.3 
120.2 
114.5 
91.9 
73.5 
97.9 
420.6 
29.9 
136.3 

12.2 

137.6 
136.2 
140.1 
116.3 
102.1 
81.5 
116.9 
112.7 
89.2 
71.8 
96.3 
475.4 
35.6 
176.7 

30.3 

Anthracite  Coal. 
Bituminous  Coal 
Lignite    

0.90 
0.85 
0.70 
0.55 
0.39 
0.85 
0  89 

0.03 
0.05 
0.05 
0.05 
0.04 
0.05 

0.03 
0.06 
0.20 
0.30 
0.50 

0.04 
0.06 
0.05 
0.10 
0.07 
0.10 
0.18 
0.01 
0.01 
0.07 

Peat   .  .  . 

Peat  0.  20  Water. 
Coke  
Peat-Charcoal 

Dry  Wood. 

0.48 
0.40 
0.80 

6.43 
0.62 

0.06 

0.06 
0.05 

i.oo 
6.2i 

0.02 

0.05 
0.25 
0.04 

'0.57' 
0.17 

0.92 

Wood  0.20  Water 
Wood-Charcoal  . 
Hydrogen  
Carbonic  Oxide 
Illuminating  Gas 
Gas   from   Blast 
Furnaces  

Mean  composition  of  combustibles,  exclusive  of  ask  ;  according  to  Percy. 


• 

Carbon. 

Hydrogen. 

Oxygen. 

Wood     ....     

49  21 

6.27 

44.52 

Peat  

54.25 

6.4 

39.35 

Bituminous  Coal     

82.59 

5.08 

12.33 

Anthracite  

94.03 

2.94 

3.03 

CHAPTER  IY. 

THE    TRANSFER    OF    HEAT. 

180.  THE  combustion  of  bodies  in  air  being  to  a  certain  ex- 
tent a  self-sustaining  process,  it  is  only  necessary  to  supply  the 
elements  of  combustion,  fuel,  and  air,  in  proper  proportions, 
and  to  ignite  the  combustible  at  one  point,  in  order  to  produce 
heat  at  will,  and  in  any  desirable  quantities.   And  the  elements 
necessary  being  almost  universally  distributed,  or  at  least  read- 
ily procurable,  there   are  scarcely  any  circumstances  in  which 
the  evolution  of  heat  for  useful  purposes  is  not  practicable. 

For  the  purposes  of  heat-power  it  is  not  practicable,  however, 
except  in  some  small  heat-engines,  to  employ  the  heated  products 
of  combustion  directly  in  the  cylinders  of  engines.  And  hence 
the  necessity  of  transferring  the  heat  of  combustion  to  water,  or 
some  other  liquid,  in  order  to  make  use  of  the  vapor  of  the 
liquid  as  the  medium  through  which  the  heat  is  utilized.  Wa- 
tery vapor  is  that  which  is  univgrsally  used,  not  only  on  account 
of  the  favorable  properties  of  this  vapor,  but  also  from  the  uni- 
versal distribution  and  cheapness  of  the  liquid,  the  expense  of 
procuring  it  being  insignificant. 

The  apparatus  for  producing  steam  under  the  ciroumstances 
required  for  use,  must  combine  therefore  the  conditions  neces- 
sary for  the  supply  of  fuel  and  air,  the  supply  of  water,  the 
transfer  of  the  heat  of  combustion  to  the  water,  and  the  reten- 
tion of  the  steam  produced. 

The  full  discussion  of  these  conditions  in  the  case  of  the 
steam-boiler  involves  the  construction  and  arrangement  of  the 
parts  of  the  boiler,  and  cannot  be  disconnected  from  them ;  but 
there  are  certain  general  principles  of  physics  which  form  the 
basis  of  such  construction  and  arrangements,  which  maybe  first 
enumerated  in  a  general  way,  such  as  the  laws  of  transfer  of 
heat,  the  temperature  of  the  products  of  combustion,  and  the 
laws  of  conduction.  < 

181.  The  Transfer  of  Heat  from  a  heated  body  to  one  that 
is  at  a  lower  temperature  consists,  according  to  the  dynamic 


TRANSFER   OF  HEAT.  95 

theory  of  heat,  in  the  loss  of  living  force,  due  to  heat-motion,  in 
the  hotter  body,  and  an  equivalent  gain  of  living  force  in  the 
colder  body.  When  the  two  bodies  are  quite  distinct,  or  sepa- 
rated, and  do  not  form  part  of  one  and  the  same  body,  this 
transfer  takes  place  generally,  as  has  been  stated,  through  the 
intervening  ethereal  medium  by  the  process  of  radiation. 
Through  this  medium  there  is  a  tendency  to  equilibrium  of 
temperature,  or  of  living  force ;  the  relative  exchange  of  tem- 
peratures being  inversely  proportional  to  the  masses  of  the 
bodies. 

It  is  probable  that  the  transfer  of  heat  between  two  bodies 
is  always  thus  accomplished  by  radiation,  although,  techni- 
cally, a  distinction  is  made  between  the  transfer  at  appreciable 
distances,  or  radiation,  and  the  transfer  by  actual  contact  of 
the  two  bodies. 

182.  Heat  may  be  transferred  practically  also  by  the  actual 
change  of  position  of  the  body  in  which  it  exists.  In  this  mode 
of  transfer,  which  is  called  convection,  or  carrying,  the  transfer 
is  a  mechanical  one,  and  is  not  in  any  way  connected  with  the 
change  of  heat  in  the  body  carried.  Although  this  mode  of 
transferring  heat  is  of  great  importance  in  the  arts,  and  espe- 
cially in  connection  with  the  generation  of  steam,  involving  as 
it  does  the  question  of  circulation  of  heated  fluids,  yet  after  the 
convection  of  heat  by  the  transfer  of  the  body  in  which  it  ex- 
ists, whether  that  body  be  solid,  liquid,  or  gaseous,  there  still 
must  take  place  the  transfer  from  the  heated  body  to  another, 
by  the  process  of  radiation  or  contact,  before  the  heat  can  be 
utilized  as  heat.  Thus  a  heated  gas  or  liquid  may  be  carried 
through  pipes,  or  may  be  mingled  mechanically  with  other 
gases  or  liquids  for  the  purpose  of  conveying  heat ;  but  the 
final  process  by  which  that  heat  is  actually  transferred  from 
the  heated  gas  or  liquid  to  another  body,  as  heat,  must  depend 
on  the  dynamic  laws  of  heat. 

In  adopting,  therefore,  the  usual  designations  of  the  modes 
by  which  heat  is  transferred,  viz ., 

Radiation, 

Contact, 

Convection, 

it  is  to  be  understood  that  the  latter  is  a  mechanical  mode, 


96  TRANSFEK   OF  HEAT. 

and  need  be  discussed  only  in  connection  with  the  carrying  of 
bodies  to  the  places  or  points  at  which  it  is  desirable  or  neces- 
sary for  them  to  impart  their  heat  to  other  bodies. 

183.  Radiation  of  Heat. — A  heated  particle  of  a  substance 
communicates  vibrations  to  the  ethereal  medium,  whether  the 
particle  be  surrounded  by  air  or  whether  it  be  in  a  vacuum.  In 
ordinary  language,  the  particle  sends  rays  of  heat  in  every  direc- 
tion ;  these  rays  or  wraves  proceed  indefinitely,  without  change 
in  strength  or  character,  and  with  the  same  velocity  as  light, 
until  they  are  intercepted  by  some  body  in  the  paths  of  the  rays. 
If  such  a  particle  be  a  molecule  on  the  surface  of  a  body,  it  is 
evident  that  it  will  send  off  rays  of  heat  in  every  direction  not 
intercepted  by  the  body  itself. 

It  is  a  common  error  to  suppose  that  the  intensity  of  a  ray 
of  heat  diminishes  as  the  distance  between  the  body  emitting 
and  the  body  receiving  the  heat  increases,  i.e.,  inversely  as  the 
square  of  the  distance.  The  same  popular  error  exists  to  a 
certain  extent  in  regard  to  the  force  of  gravitation ;  whereas 
the  greatest  conceivable  distances  have  apparently  no  effect  in 
retarding  or. diminishing  the  effects  of  the  influences  called  heat 
and  gravitation. 

The  law  of  the  inverse  squares  of  the  distances  is  rather,  a 
geometrical  than  a  physical  law,  and  refers  to  the  action  of  one 
l)ody  on  another,  whether  the  question  be  one  of  heat  or  gravita- 
tion. 

A  body  or  collection  of  molecules  possessing  a  certain 
amount  of  living  force,  due  to  heat,  imparts  this  energy  to  the 
ethereal  medium  in  all  directions,  and  the  quantity  of  energy 
intercepted  by  another  body  will  depend  on  the  distance  be- 
tween the  two  bodies ;  the  quantity  thus  intercepted  by  the 
same  body  at  different  distances  being  inversely  proportional 
to  the  squares  of  the  distances. 

This  purely  geometrical  law  may  be  illustrated  by  the  follow- 
ing sketch : 

Suppose  P  to  be  a  heated  body  giving  off  radiant  heat  in 
every  direction.  Another  body,  a  plate  for  instance,  placed  at 
distances  1,  2,  3,  4,  5,.  .  .from  the  heated  body,  will  intercept 
less  of  this  heat  as  it  is  removed  from  the  heated  body,  the 
number  of  rays,  or  quantity  of  heat,  intercepted  at  two  different 
distances  being,  from  the  geometrical  conditions  of  the  problem, 
inversely  proportional  to  the  squares  of  those  distances. 


TRANSFER   OF  HEAT. 
FIG.  2. 


The  absurdity  of  supposing  that,  because  the  mathe- 
matical result  of  reducing  the  distance  to  zero  is  a  symbol  of 
infinity,  therefore  the  physical  influence  at  that  distance  is 
infinite,  need  not  be  discussed,  although  such  an  assumption 
is  often  made  in  attempts  to  discuss  the  intensity  of  molecular 
forces. 

When,  therefore,  it  is  said  that  the  intensity  of  radiant  heat 
varies  inversely  as  the  square  of  the  distance,  all  that  is  meant 
"is,  that  the  same  body,  placed  at  different  distances  from  the 
same  source  of  heat,  will  receive,  in  a  given  time,  by  radiation, 
different  quantities  of  heat  in  the  inverse  proportion  of  the 
squares  of  the  distances.  In  going  away  from  a  glowing  fire 
in  our  grates,  for  instance,  we  receive  less  and  less  heat,  be- 
cause, as  the  distance  is  increased,  we  pass  out  of  the  paths  of 
large  numbers  of  divergent  rays  which  would  otherwise  reach 
us. 

184.  The  inclination  of  the  surface  which  intercepts  radiant 
heat  determines,  for  similar  reasons,  the  quantity  of  radiant  heat 
received.  Even  if  the  rays  be  supposed  parallel,  as  in  the  case 
of  the  radiant  heat  of  the  sun,  it  is  apparent  that  all  the  heat 
conveyed  by  a  beam  of  rays  may  be  represented  by  the  section  of 
the  beam  perpendicular  to  its  direction.  If  the  beam  falls  upon 
a  surface  inclined  to  its  direction,  the  amount  of  surface  over 
which  the  beam  will  be  distributed  will  be  greater  as  the  in- 
clination of  the  surface  is  greater.  If  the  surface  be  plane,. 
7 


OS  TRAHSFEK  OF  HEAT. 

when  it  becomes  parallel  to  the  axis  of  the  beam,  it  will  receive 
no  heat. 

Hence  in  estimating  the  intensity  of  radiant  heat  by  units  of 
surface,  the  inclination  of  the  receiving  and  absorbing  surfaces 
must  be  considered. 

The  regions  of  the  earth's  surface  near  the  poles,  from  their 
approach, to  parallelism  with  the  direction  of  the  sun's  beams, 
receive  little  heat  on  each  square  mile  of  surface,  compared 
with  the  quantity  received  by  a  square  mile  at  the  tropics. 

185.  If  a  heated  body  be  placed  within  an  enclosed  space,  it 
is  evident  that  although  some  parts  of  the  enclosure  may  receive 
more  heat  per  square  foot  than  others,  yet  all  the  heat  emitted 
will  be  absorbed. 

All  the  heat  emitted  by  radiation  from  the  incandescent  fuel 
on  the  grate  of  the  furnace  of  a  steam-boiler  is  thus  absorbed 
by  the  side  walls  and  crown  of  the  furnace,  though  in  different 
proportions  per  square  foot. 

186.  Attempts  have  been  made  to  determine  the  quantity  of 
heat  in  units  of  heat  emitted  by  any  given  surface  at  a  given 
temperature,  supposing  the  temperature  of  the  absorbing  sur- 
faces to  remain  at  constant  temperature. 

MM.  Dulong  and  Petit,  whose  researches  in  this  and  other 
branches  of  physics  are  universally,  known,  made  numerous  ex- 
periments on  this  subject,  which  resulted  in  the  determination 
of  certain  general  laws.  The  experiments  were  made  to  deter- 
mine the  rate  of  cooling  of  bodies  in  an  enclosed  space,  the 
space  being  filled  with  different  gases,  and  the  enclosure  being 
maintained  at  constant  temperature. 

The  results  were  enunciated  as  follows : 

1.  "  The  cooling  of  a  body  results  from  radiation  and  from 
contact  of  the  fluid  or  gas  which  surrounds  it. 

2.  "  The  rate  of  cooling,  from  radiation  alone,  is  the  same  for 
all  bodies  at  the  same  temperature,  but  its  absolute  value  de- 
pends on  the  nature  of  the  surfaces." 

It  is  represented  by  the  following  formula  : 

Q  =  o.  a*  (afcl  --  1)  or  Q  =  o,  (at]  —  1) 

in  which  Q  represents  the  number  of  French  units  of  heat  emit- 
ted by  one  unit  of  surface  in  a  unit  of  time,  c  a  constant  depend- 
ing on  the  nature  of  the  surface  of  the  radiant  body,  a,  the 


TKANSFER    OF  HEAT. 


99 


number  1.0077,*  t  the  temperature  of  the  enclosure  or  absorb- 
ant,  and  tj  the  excess  of  temperature  of  the  radiating  body  over 
the  absorbing  body  in  degrees  Centigrade. 

3.  "  The  rate  of  cooling  by  contact  of  a  fluid  surrounding  the 
heated  body  is  also  the  same  for  all  heated  bodies,  but  its 
absolute  value  does  not  depend  on  the  nature  of  the  surface, 
and  depends  only  on  the  form  of  the  heated  body."f 

For  air  under  ordinary  atmospheric  pressure  the  law  of  cool- 
ing by  contact  is  expressed  by  the  formula 


Q  =  c't 


1.233 


in  which  Q  represents  the  quantity  of  heat  in  calories  abstracted 
from  one  unit  of  surface  by  the  air  in  a  unit  of  time,  c'  a  con- 
stant depending  on  the  form  of  the  surface,  and  t  the  excess 
of  temperature  of  the  body  over  that  of  the  air  surrounding  it. 
187.  These  general  laws  were  confirmed  by  Peclet,  who  made 
many  experiments  to  determine  the  constant  co-efficients  of  the 
formulas.  Similar  experiments  have  more  recently  been  made 
also  by  Mr.  Hopkins,  whose  results  are  as  follows,  for  radiation 
alone : 

For  Glass. 
Q  =  9.566.  a*  (a*1  -  1) 


Dry  Chalk. 
Q  =  8.613  a*  (atj  - 


Dry  New  Red  Sandstone. 
Q  =  8.377  a^a*1  -1) 

Polished  Limestone. 
Q  =  9.106  a*  (a*1  -  1) 


*  It  was  proved  by  De  la  Provostaye  and  Desains  that  a  differs  for  different 
bodies, 
t  Peclet. 


100  TRANSFER  OF  HEAT. 

In  which  Q  represents  the  quantity  of  heat  emitted  in  one 
minute  from  one  square  foot  of  surface,  in  terms  of  a  unit  which 
is  the  quantity  of  heat  required  to  raise  the  temperature  of 
1,000  grams  of  water  1°  Centigrade. 

Mr.  Hopkins  also  determined  by  experiment  the  constants  in 
the  formula  for  the  cooling  power  of  gases  by  contact,  the  re- 
sults of  which,  as  given  below,  are  also  quoted  from  Balfour 
Stewart. 

For  Atmospheric  Air. 

.45 


For  Hydrogen. 


1.238 


For  Carbonic  Acid. 


For  Olefiant  Gas. 


p  representing  the  pressure  of  the  gas  in  millimetres. 

188.  In  regard  to  these  formulas,  it  may  be  doubted  whether 
the  experiments  were  made  in  such  a  manner  as  to  lead  to  results 
of  practical  value.     The  constants  determined  by  Peclet,  and  by 
Hopkins,  can  only  refer  to  the  special  conditions  under  which 
the  experiments  were  made,  which  conditions  are  not  those  ad- 
mitting of  general  application.     Moreover,  the  separating  of  the 
influences  of  radiation  and  contact  in  the  experiments  does  not 
seem  to  have  been  sufficiently  complete. 

189.  The  only  results  of  value  seem  to  be  the  general  laws,  as 
enunciated,  without  reference  to  quantities  of  heat. 

The  relative  radiating  powers  of  different  surfaces  at  180° 
Fahrenheit,  as  determined  by  Leslie,  are  represented  approxi- 
mately in  the  following  table  :* 

*  Watts's  Die.  of  Chemistry. 


TRANSFER  OF  HEAT.  101 

Lampblack 100  Mica 80 

Paper 98  Graphite 75 

Eesin 96  Tarnished  lead 45 

Sealing-wax 95  Mercury 20 

Crown  glass 90  Polished  lead 19 

India  ink 88  Polished  iron. ......  15 

Ice 85  Tin  plate 12 

Red  lead 80  Gold,  silver,  copper .  12 

Experiments  by  Magnus  give  the  following  relative  emissive 
powers  for  different  surfaces  at  270°  Fahr. : 

Blackened  silver 100 

Glass 64 

Fluor-spar 45.5 

Eock  salt 13 

Polished  silver 9.7 

It  is  stated  by  Magnus  that  the  greater  or  lesser  density  of 
the  surface  has  no  influence  on  radiation  from  the  surface.  Pla- 
tinum which  has  been  strongly  hammered,  possesses  the  same 
emissive  power  as  platinum  carefully  annealed.  But  the  same 
surface  roughened  with  emery-paper  has  its  emissive  power 
greatly  increased.  As  far  as  quantities  of  heat  are  concerned,  it  is 
doubtful  whether  anything  further  than  such  relative  determi- 
nations can,  in  the  present  state  of  knowledge,  be  depended  on ; 
the  actual  or  absolute  quantities  for  different  temperatures  being 
still  uncertain. 

190.  The  laws  of  radiation  which  have  been  enunciated  point 
out,  however,  one  fact  which  has  an  important  bearing  in  connec- 
tion w^ith  the  transfer  of  heat.  The  formula  Q  =  c.  a  (a  ,  —  1) 

or  c,  (a  i  —  1)'  shows  that  the  differences  of  temperatures  of  the 
radiant  and  absorbing  bodies  enter  as  exponents  in  the  formula, 
so  that  with  a  constant  temperature  of  the  absorbent  body,  such 
as  the  water  over  the  furnace  in  steam-boilers,  the  quantity  of 
heat  emitted  by  the  grate,  and  absorbed  by  the  water,  will  in- 
crease with  great  rapidity  as  the  temperature  of  the  fire  in- 
creases. The  formula  for  the  cooling  of  the  gaseous  products  of 
combustion,  on  the  other  hand,  Q  =  c'  t/-*33  shows,  if  this 
law  be  true,  that  the  influence  of  increase  of  temperature  in  the 


102 


TRANSFER  OF  HEAT. 


gases  is  not  so  great  as  111  radiation,  because  the  difference  of 
temperature  between  the  heated  gases  and  the  water  of  the 
boiler  is  simply  raised  to  the  power  indicated  by  the  constant 
exponent  1.233. 

191.  These  formulas  serve  to  illustrate,  by  curves,  the  emis- 
sion of  heat,  in  English  imits,  by  radiation  and  contact  of  a  gas, 
the  absorbent  of  the  heat  being  maintained  at  constant  tem- 
perature, and  the  temperature  of  the  heated  body,  whether  a 
radiating  solid  or  a  gas,  being  gradually  increased. 

Diagram  illustrating  the  emission  of  heat  by  radiation  and 
~by  contact  of  gases. 


FIG.  3. 


153498 .. 


2168. 


In  the  above  diagram  the  lower  horizontal  line  represents 
differences  of  temperature,  in  Fahr.  degrees,  between  the  heated 
gas  or  radiating  body,  and  the  absorbing  body.  The  vertical 
line  b  c  represents  English  units  of  heat  transferred  to  an  ab- 
sorbent at  constant  temperature.  The  ordinates  of  the  curve 
a  b  represent  heat  transferred  by  contact  of  gases,  according  to 


TRANSFER  OF  HEAT.  103 

the  law  Q  =  GI  t,1-233  and  the  ordinates  of  the  curve  a  c,  the  heat 

transferred  by  radiation,  according  to  the  law  Q,  =  Cj  (a  l  —  1). 
These  quantities  have  been  calculated,  according  to  the  best 
data,  for  the  conditions  presented  in  the  furnace  and  flues  of  a 
steam-boiler.  For  small  differences  of  temperature  the  two 
curves  are  nearly  identical.  For  a  difference  of  400°  the  heat 
absorbed  by  the  plates  from  contact  of  gases  will  be,  for  unit 
of  surface  and  unit  of  time,  922,  and  from  radiation  6821.  For 
a  difference  of  temperature  of  800°  the  heat  absorbed  from  con- 
tact of  the  gases  in  unit  of  time  and  for  unit  of  surface,  found 
by  calculation,  is  2168,  and  for  the  same  difference  of  tempera- 
ture the  heat  absorbed  from  radiation  is  153498  units. 

This  application  of  the  laws  of  Dulong  and  Petit  is  made  on 
the  supposition  that  the  law  of  cooling  by  radiation  is  the  re- 
ciprocal of  the  law  of  absorption  of  radiant  heat,  and  the  law 
of  cooling  by  contact  of  a  colder  gas  is  the  reciprocal  of  the 
law  of  heating  by  contact  of  a  hot  gas ;  the  direction  of  the 
transfer  of  heat  being  a  matter  of  indifference.  The  diagram 
is  drawn  from  a  larger  one  constructed  from  calculated  ordi- 
nates, and  is  given  merely  to  illustrate  the  great  difference  be- 
tween the  transfer  of  heat  by  radiation  and  contact  for  large 
differences  of  temperature  between  the  heating  and  absorbing 
bodies.  Thus,  according  to  these  calculations,  the  quantity  of 
heat  transferred  or  absorbed  by  one  square  foot  of  surface  from 
a  radiating  body,  with  a  difference  of  temperature  of  800°,  is 
over  70  times  the  quantity  absorbed  from  heated  gases  in  the 
same  time  with  the  same  difference.  These  illustrations  are 
made  on  the  supposition  that  the  difference  of  temperature  re- 
mains constant  for  a  given  time. 

In  the  radiation  of  heat,  such  as  the  radiation  from  the  heated 
fuel  of  a  furnace,  this  constancy  of  temperature  is  kept  up  usually 
by  the  progress  of  the  combustion.  But  in  heated  gases  the 
constancy  of  the  difference  of  temperature,  or  the  high  tem- 
perature of  the  gas  in  contact  with  any  given  portion  of  sur- 
face, can  be  maintained  only  by  the  removal  of  the  cooled  gas 
and  the  renewal  of  heated  gas  from  the  furnace. 

This  involves  the  question  of  the  circulation  of  gas  and  the 
convection  of  heat— elements  of  the  problem  which  render  the 
determination  of  constants  for  the  formulas  doubtful. 

192.  Action  of  Bodies  on  Radiant  Heat. — Light  and  radiant 
heat  are  now  assumed  by  philosophers  to  be  manifestations  of 


104  TRANSFER  OF  HEAT. 

the  same  physical  agent ;  and  heat,  like  light,  when  it  falls 
upon  the  surface  of  a  body  may  be  reflected,  refracted,  ab- 
sorbed, or  polarized. 

The  radiating  powers  of  different  bodies,  or  different  sur- 
faces, represent  also  their  absorptive  powers,  and,  as  has  been 
already  stated,  radiant  heat  does  not  affect  the  eye,  or  solids  do 
not  become  luminous,  until  the  temperature  reaches  about 
750°  Fahr. 

193.  The  radiation  and  absorption  of  gases,  according  to  Pro- 
fessor Tyndall,  present  very  peculiar  laws,  and  our  knowledge 
of  the  action  of  gaseous  bodies  on  radiant   heat  is  still  very 
slight.     It  has  been  demonstrated  experimentally  by  Professor 
Tyndall  that  a  ray  or  beam  of  heat  is  wholly,  or  almost  wholly, 
transmitted  through  moderate  distances  in  air,  oxygen,  hydro- 
gen, and  nitrogen ;  and  conversely,  no  radiation  takes  place 
from   the   heated   particles   of  these  gases.     The  only  mode, 
therefore,  by  which  heat  can  be  imparted  to  these  gases,  or  by 
which  they  can  impart  heat  to  other  bodies,  is  by  actual  contact. 

Some  other  gases  possess  remarkable  powers  in  absorbing  or 
intercepting  dark  radiant  heat. 

194.  The  absorption  of  radiant  heat  by  vapor  of  water  dif- 
fused in   air,  under  circumstances  of  average  humidity,  was 
shown  by  Professor  Tyndall  to  be  70  times  greater  than  the  ab- 
sorption by  dried  air.     As  the  quantity  of  watery  vapor  was  in- 
creased, the  amount  of  heat  absorbed  was  increased. 

This  fact  has  been  suggested  by  Mr.  C.  E.  Emery,  a  practical 
engineer  of  !N".  Y.,  to  be  an  important  cause  of  loss  of  heat  in 
the  cylinders  of  steam-engines,  when  there  is  condensation  in 
the  cylinder.  The  walls  of  the  cylinder  radiate  heat  to  the 
cloudy  vapor  and  become  cooled,  the  heat  radiated  being 
carried  out  with  the  exhaust ;  and  when  new  steam  is  again  ad- 
mitted the  walls  are  again  re-heated  by  the  incoming  steam. 

Comparative  experiments,  made  with  glass  and  iron  cylin- 
ders, seemed  to  confirm  this  view,  glass  being  a  feeble  radiator 
and  absorber.  Acting  on  this  ide/a,  Mr.  Emery  pr6posed  a 
mechanical  separator  to  the  double-cylinder  engine,  to  remove 
the  particles  of  water  from  the  steam  in  its  passage  from  the 
smaller  to  the  larger  cylinder. 

As  the  quantity  of  watery  vapor  contained  in  air  at  different 
temperatures  is  often  a  matter  of  importance  in  technical  ap- 
plications, and  especially  when  taken  in  connection  with  the 


TRANSFER  OF  HEAT. 


105 


radiation  of  heat,  the  following  table  is  here  introduced, 
showing  the  quantities  of  watery  vapor  in  air  at  dew-points 
from  0°  to  100°  Fahr. : 


TABLE  XXV. 


Deg. 
Fahr. 

Grains  in  a 
cu.  foot. 

Deg. 
Fahr. 

Grains  in  a 
cu.  foot. 

Deg. 
Fahr. 

3-rains  in  a 
cu.  foot. 

Deg. 
Fahr. 

Grains  in  a 
cu.  foot. 

Deg. 
Fahr. 

Grains  in  a 
cu.  foot. 

0 

0.186 

21 

1.618 

42 

3.274 

63 

6.400 

84 

12.079 

1 

0.810 

22 

1.674 

43 

3.382 

64 

6.620 

85 

12.439 

2 

0.836 

23 

1.733 

44 

3.495 

65 

6.810 

86 

12.808 

8 

0.864 

24 

1.793 

45 

3.610 

66 

7.024 

87 

13.185 

4 

0.893 

25 

1.855 

46 

3.729 

67 

7.243 

88 

13.577 

5 

0.925 

26 

1.915 

47 

3.851 

68 

7.469 

89 

13.977 

6 

0.957 

27 

1.986 

48 

3.979 

69 

7.702 

90 

14.387 

7 

0.992 

28 

2.054 

49 

4.109 

70 

7.941 

91 

14.809 

8 

1.028 

29 

2.125 

50 

4.244 

71 

8.186 

92 

15.241 

9 

1.065 

30 

2.197 

51 

4.382 

72 

8.439 

93 

15.684 

10 

1.103 

31 

2.273 

52 

4.524 

73 

8.699 

94 

16.140 

11 

1.143 

32 

2.350 

53 

4.671 

74 

8.966 

95 

16.607 

12 

1.184 

33 

2.430 

54 

4.822 

75 

9.241 

96 

17.086 

13 

1.226 

34 

2.513 

55 

4.978 

76 

9.523 

97 

17.577 

14 

1.270 

35 

2.598 

56 

5.138 

77 

9.813 

98 

18.081 

15 

1.315 

36 

2.686 

57 

5.303 

78 

10.111 

99 

18.598 

16 

1-361 

37 

2.776 

58 

5.473 

79 

10.417 

100 

19.129 

17 

1.409 

38 

2.870 

59 

5.648 

80 

10.732 

18 

1.459 

39 

2.996 

60 

5.828 

81 

11.055 

19 

1.510 

40 

3.066 

61 

6.013 

82 

11.388 

20 

1.563 

41 

3.168 

62 

6.024 

83 

11.729 

195.  The  fact  that  air  charged  with  moisture  absorbs,  in  each 
unit  of  time,  70  times  more  heat  than  air  practically  dry,  is  an 
explanation  of  a  phenomenon  which  has  an  important  bearing 
on  human  health  and  comfort.   When  air  at  a  hiyh  temperature 
is  overloaded  with  moisture,  radiation  takes  place  from  the  air  to 
the  body,  producing  an  oppressive  sensation  of  heat.    When,  on 
the  other  hand,  the  temperature  of  saturated  air  is  lower  than  the 
natural  temperature  of  the  body,  the  radiation,  or  transfer  of 
heat,  will  take  place  from  the  body  to  the  air,  producing  the  sen- 
sation of  cold.     It  is  this  that  makes  a  low  temperature,  with  a 
dry  atmosphere,  more  bearable  than  a  higher  temperature  with 
air  highly  charged  with  moisture. 

196.  Transfer  of  Heat  by  Contact. — This  subject  has  been 
partially  discussed  in  connection  with  radiation. 

Definite  knowledge  on  this  subject,  in  reference  to  quantities 
of  heat,  would  be  of  greater  value,  practically,  than  a  knowledge 

*  Encyclopedia  Britannica. 


106  TRANSFER  OF  HEAT. 

of  the  exact  laws  of  radiation,  because  in  nearly  all  cases  the 
quantity  of  radiating  surface,  in  the  evolution  of  heat  by  com- 
bustion, depends  on  the  quantity  of  incandescent  surface  of  the 
fuel,  the  size  of  furnace,  and  form  of  bed  of  fuel ;  which  quan- 
tities are  dependent  on  the  quantity  of  heat  required  per  hour, 
and  are  thus  fixed  by  other  conditions  than  the  laws  of  radiation. 
But  the  utilization  of  the  heat  in  the  gaseous  products  of  com- 
bustion requires  special  constructions  of  flues  and  pipes  which, 
while  conveying  these  gases  to  the  chimneys,  act  at  the  same 
time  as  heating  surfaces  for  liquids  in  contact  with  the  surfaces. 
When  heated  gases,  or  liquids,  are  conveyed  in  pipes  or  conduits 
to  the  places  where  the  heat  is  to  be  given  off  by  contact  or  radi- 
ation from  metallic  surfaces,  the  utilization  of  heat  involves  the 
laws  of  transfer  by  contact,  and  the  determination  of  the  neces- 
sary amount  of  surface  in  such  case  is  often  directly  depend- 
ent on  these  laws.  The  quantity  of  heating  surfaces  of  steam- 
boilers,  the  cooling  surfaces  of  condensers,  the  quantity  of  sur- 
face of  hot-water  pipes  for  heating  air  for  dwellings  and  facto- 
ries,— questions  which  are  continually  presented  to  the  engineer, 
— are  dependent  on  the  action  of  these  surfaces  in  transferring, 
by  contact,  the  heat  of  a  liquid  or  gas  on  one  side  of  a  surface 
to  a  liquid  or  gas  on  the  other  side. 

197.  It  may  be  regarded  as  a  rule  that  when  the  liquids  or 
gases  on  the  opposite  sides  of  a  metallic  plate  remain  at  con- 
stant temperatures,  respectively,  the  thickness  of  the  plate  does 
not  affect  the  rate  of  transfer  of  heat  from  one  side  to  the  other. 
It  is  only  when  the  temperatures  of  the  fluids  on  the  opposite 
sides  are  changing,  that  the  internal  conductivity  of  the  wall  be- 
tween them,  or  the  dissipation  of  heat  by  the  wall,  need  be  con- 
sidered. 

Thus  the  influence  of  the  thickness  of  the  metallic  flues  of  a 
steam-boiler  is  felt  only  in  retarding  the  rapidity  of  flrst  gener- 
ating steam  after  the  fires  are  started.  After  the  boiler  is  "  in 
train,"  i.e.,  working  steadily  at  a  given  pressure,  the  greater  or 
lesser  thickness  of  the  metallic  plates  which  transmit  the  heat  to 
the  water,  is  a  matter  of  little  importance,  as  far  as  the  rate  of 
transfer  is  concerned.  This  fact  was  experimentally  demon- 
strated by  Boutigny,  and  has  been  confirmed  by  the  direct  ob- 
servations of  others. 

198.  It  is-  stated  by  Rankine  that  the  following  empirical 
formula  gives,  approximately,  the  rate  of  transfer  of  heat  per 


TRANSFER  OF  HEAT.  107 

hour  for  each  square  foot  of  heating  surface  of  the  tubes  or  flues 
of  steam-boilers : 


in  which  t^—  t  is  the  difference  of  temperature  between  the 
heated  gases  on  one  side  at  any  point,  Q  the  quantity  of  heat 
transferred  in  units  of  heat,  and  a  a  constant,  the  value  of  which 
lies  between  160  and  200. 

This  formula  is  intended  only  as  a  rough  approximation.  As 
it  is  stated  by  Rankine  to  be  the  results  of  experiments  on  the 
evaporative  powers  of  boilers,  it  is  probably  applicable  only  to 
the  special  conditions  of  those  experiments. 

If  we  regard  the  water  in  the  boiler  as  the  absorbent  of  the 
heat — the  sides  of  the  flues  being  the  walls  of  the  chambers 
which  separate  the  water  from  the  heated  gases — the  application 
of  the  law  of  Dulong  and  Petit  would  give  the  quantity  trans- 
ferred by  each  square  foot  in  an  hour  as  follows : 

Q  =  c.  (tt  -  t)1-233 

differing  from  Eankine's  formula  only  in  the  exponent. 

All  that  is  known  definitely  on  this  subject,  at  present,  ap- 
pears to  be  that  the  transfer  is  proportional  to  the  difference  of 
temperature  raised  to  a  power  greater  than  unity,  probably 
between  1  and  2. 

The  greatest  difficulty  in  applying  either  law  lies  in  the  in- 
determinate constant  coefficient. 

In  all  cases  of  heating  or  cooling  a  fluid,  by  contact  with  a 
surface,  the  quantity  of  heat  transferred  in  a  unit  of  time  de- 
pends 011  the  circulation  of  the  fluid ;  and  where  one  fluid  is 
heated  or  cooled  by  another,  the  two  fluids  being  separated  by  a 
metallic  plate,  the  circulation  of  both  fluids  must  be  taken  into 
consideration.  This  is  the  condition  under  which  the  heat  of 
the  gaseous  products  of  combustion  in  the  steam-boiler  is  trans- 
ferred to  the  water.  Want  of  circulation  in  either  the  heated 
gases,  or  the  water,  causes  a  retardation  or  complete,  suspension 
of  the  transfer  of  heat. 

199.  When  heat  is  thus  transferred  by  contact  from  one  fluid, 
either  liquid  or  gaseous,  to  another,  through  a  metallic  plate,  it 


108  TRANSFER  OF  HEAT. 

results,  from  the  law  that  the  quantity  transferred  depends  on 
the  difference  of  temperatures,  that  the  motions  of  the  two  fluids 
should  be  in  opposite  directions.  The  difference  of  tempe- 
ratures will  then  be  the  greatest  possible  at  every  point. 

200.  Heating  surface  is  an  expression  used  to  designate,  in 
mechanical  constructions,  the  surfaces  or  plates,  usually  metallic, 
through  which  heat  is  transmitted.  Where  the  transfer  is  by 
the  contact  of  a  fluid,  as  in  the  flues  of  steam-boilers  and 
cooling  surfaces  of  condensers,  the  heating  or  cooling  fluid  is 
supplied  in  a  continuous  current,  or  stream,  through  the  flues  or 
pipes.  In  such  cases  the  fluid  usually  issues  from  the  apparatus 
at  a  constant,  determinate  temperature.  This  temperature  will 
depend  on  the  initial  temperature  and  the  specific  heat  of  the 
fluid ;  and  the  total  quantity  of  heat  transferred  from  or  to  the 
fluid,  as  it  passes  through  the  apparatus,  will  be  represented  by 
the  following  expression : 

Qi  =  Ci  (ti-  t)  x  w 

in  which  Qt  represents  now,  not  the  heat  transferred  from  a  par- 
ticular square  foot  of  surface  in  a  unit  of  time,  but  the  whole 
heat  abstracted  from,  or  imparted  to,  the  circulating  fluid  in  a 
unit  of  time  ;  ^  —  t  represents  the  loss  or  gain  of  temperature 
of  this  fluid,  and  w  the  total  weight  of  the  fluid  which  passes 
through  the  apparatus  in  a  unit  of  time. 

The  volume  of  fluid  which  passes  through  the  apparatus  will 
be  proportional  to  the  velocity  multiplied  by  the  total  sectional 
area  of  the  flues  or  pipes  through  which  it  passes  ;  and  since 
the  weight  is  equal  to  the  volume  multiplied  by  the  density,  or 
w  =  v  DJ,  it  is  evident  that  it  will  require  a  much  greater  vol- 
ume of  a  gas  to  impart  or  abstract  a  given  quantity  of  heat  than 
a  liquid. 

If  a  given  quantity  of  heat  is  to  be  transferred  by  an  appa- 
ratus, through  the  medium  of  fluid  contact,  in  a  given  time,  that 
quantity  being  represented  by 

Ql  =  Cl  w  (tt  -  t) 
or,  Ql  =  Cl  v  D  (ti  -  t) 

It  appears,  therefore,  that  the  volume  of  the  fluid,  its  density, 


TRANSFER  OF  HEAT.  109 

its  specific  heat,  and  the  initial  and  final  temperatures,  must 
all  be  considered. 

Where  the  initial  and  final  temperatures  of  the  circulating 
fluid  are  fixed  by  the  conditions  of  the  problem,  the  quantities 
to  be  considered  will  be  the  specific  heat,  the  volume,  and  the 
density  of  the  fluid. 

For  given  volumes  of  flow,  liquids  are,  therefore,  under  such 
conditions,  more  efficient  than  gases  in  proportion  to  their 
greater  density. 

201.  Conduction  of  Heat.  —  Conduction  of  heat  refers  to  the 
transmission  of  heat  from  one  part  of  a  continuous  and  homo- 
geneous body  to  another  part  of  the  same  body.  When  a  body 
is  heated  at  one  point,  the  heat  is  transmitted  with  greater  or 
less  rapidity  throughout  the  whole  mass,  depending  on  the 
nature  of  the  body  and  the  differences  of  temperature  of  the 
heated  part  and  other  parts  of  the  body.  If  the  body  is  ter- 
minated by  two  parallel  surfaces,  which  are  each  kept  at  a  con- 
stant temperature,  there  will  be  a  flow  of  heat,  so  to  speak,  at  a 
constant  rate,  from  the  hotter  surface  to  the  other  by  conduc- 
tion. 

The  law  of  conduction  under  these  circumstances  is,  that  the 
quantity  transmitted  for  a  unit  of  area  perpendicular  to  the 
direction  of  transmission,  and  per  unit  of  time,  is  directly  pro- 
portional to  the  difference  of  temperatures  of  the  parallel  sur- 
faces, and  inversely  proportional  to  the  thickness  or  distance 
which  separates  the  two  surfaces.  If  tt  and  t  represent  the 
temperatures  of  the  two  surfaces,  and  e  the  distance  separating 
them,  the  quantity  of  heat  transmitted  will  be  represented 
algebraically  by  the  formula 


_ 

Q- 


The  coefficient  c  depends  on  the  nature  of  the  body. 

When  the  quantities  of  heat  thus  transmitted,  for  different 
bodies,  across  an  interval  one  unit  of  length  in  thickness,  and 
for  one  unit  of  area  and  time,  are  determined,  these  quantities 
of  heat  represent  the  relative  conductibilities  of  the  substances, 
and  the  numbers  thus  found,  when  referred  to  one  as  a  stand- 
ard, may  be  called  the  conductivities  of  the  different  sub- 
stances. 


HO  TRANSFER   OF   HEAT. 

202.  The  relative  conductivities  of  metals  determined  by  ex- 
periments on  bars  of  a  given  cross-section,  the  transmission  of 
heat  being  determined  by  thermometers  placed  at  different  dis- 
tances in  holes  drilled  in  the  bars,  have  been  ascertained  by  dif- 
ferent investigators. 

The  following  table  of  conductivities,  from  experiments  made 
by  MM.  Wiedemann  and  Franz,  the  temperatures  along  the 
bars  being  determined  by  a  thermo-electric  arrangement,  is 
given  by  Balfour  Stewart : 


TABLE  XXVI. 

, Relative  Conductivities % 

Name  of  Metal.  In  Air.  In  Vacuo. 

Silver 100 100. 

Copper 73.6  74.8 

Gold -. 53.2  54.8 

Brass 23.6  24. 

Tin 14.5 15.4 

Iron 11.9  10.1 

Steel 11.6  10.3 

Lead 8.5  7.9 

Platinum 8.4  7.4 

Palladium  . . .- 6.3  7.3 

Bismuth 1.8  

It  was  found  by  Professor  Forbes  that  the  conductivity 
diminishes  as  the  temperature  of  the  metal  increases.  For  iron, 
the  diminution  of  the  number  representing  the  conductivity 
was  from  15  to  25  per  cent,  for  an  increase  of  100°  tempera- 
ture. 

It  was  shown  also  by  Professor  Forbes  that  the  same  num- 
bers show  the  relative  conductivity  for  electricity. 

For  the  absolute  quantities  of  heat,  in  thermal  units,  trans- 
mitted, the  following  table,  from  Watts's  Die.  of  Chemistry,  gives 
the  most  reliable  data  for  a  few  substances. 

In  this  table  the  numbers  and  formulas  give  the  quantities 
of  heat  in  calories  (kilogram-degrees)  which  will  pass  through 
a  metallic  plate  1  millimetre  in  thickness  and  1  square  metre 
in  area,  in  1  second,  when  the  temperatures  of  the  two  parallel 
surfaces  differ  by  1°  Centigrade. 


TRANSFER   OF  HEAT. 


Ill 


TABLE  XXVII. 


Observer. 

.Name  or  feubstance. 

Angstrom. 

Neumann, 

102.7  (1  —  0.003567t) 

110.75 

30.70 

30.19 

19.88  (1  —  0.00479t) 

16.37 

10.94 

By  Peclet. 

3'.84 

The  results  of  Neumann,  reduced  to  English  units  of  heat 
and  English  units  of  area,  thickness,  and  time,  will  give  the 
approximate  numbers  in  the  following  table  for  the  quantity 
of  heat  transmitted  per  second,  by  conduction,  through  an  area 
of  1  square  foot,  and  a  thickness  of  1  millimetre,  or  .0394  of 
an  inch,  the  difference  of  temperatures  between  the  parallel 
faces  of  the  plate  being  1°  Fahrenheit : 


Copper. 
Zinc. . . 
Brass . . 
Iron. . 


German  Silver 4.1 

Lead..  1.4 


The  relative  thermal  resistance,  or  reciprocal  of  the  conduc- 
tivity, of  liquids,  as  determined  by  Professor  Guthrie,*  is  given 
in  the  following  table,  for  the  liquids  named : 

Water 1.0 

Glycerine 3.84 

Acetic  Acid 8.38 

Sperm  Oil 8.85 

Alcohol 9.09 

Oil  of  Turpentine 11.75 

The  absolute  values  of  the  conductivities  of  liquids  are  uncer- 
tain. It  was  ascertained  by  Professor  Guthrie,  however,  that 


*  Phil.  Transactions,  1809. 


112  TRANSFER  OF  HEAT. 

the  conducting  power  of  liquids  is  greater  at  high  temperatures 
than  at  'low  temperatures.  And  when  there  is  no  convection  of 
heat  in  liquids,  by  which  heated  particles  are  carried  from  one 
point  to  another,  the  conducting  power  of  liquids  is  very  small  ; 
the  conducting  power  of  water  being,  according  to  Depretz, 
only  about  T^¥  that  of  copper. 

203.  Conduction  by  Gases.  —  Gases  possess  such  a  feeble 
power  of  conduction  that  they  have  been  regarded  as  having  no 
conducting'  power.  Experiments  by  Magnus,  and  theoretical 
deductions  by  Clausing,  however,  demonstrate  that  there  is  a 
slight  power  of  conduction  in  perfect  gases. 

Clausius  estimates  the  conducting  power  of  air  to  be  about 


204.  Temperature  accompanying  Combustion.  —  The  cal- 
orific intensity  of  combustion,  or  degree  of  temperature  of  the 
products  of  combustion,  and  of  the  solid  incandescent  combusti- 
ble, seems  to  depend  on  the  rapidity  of  combustion  rather  than 
the  quantity  of  heat  evolved.  Nearly  all  writers  on  the  subject 
have  given  a  method  for  find  ing  what  may  be  called  the  theo- 
retical temperature  of  combustion,  by  supposing  that  all  the  heat 
evolved  is  contained  in  the  gaseous  products,  and  calculating 
the  temperature  by  means  of  the  specific  heats,  and  the  weights 
of  the  products  of  combustion,  and  the  heat  evolved,  —  making 
use  of  formulas  corresponding  to  that  which  has  already  been 
given,  page  10,  viz.  : 

Q  =  w  x  c  x  F 

Q  representing,    in    units    of  heat,  the  heat  evolved,    w    the 
weight,  and  c  the  specific  heat  of  the  gaseous  products  of  com- 
bustion, and  F  the  number  of  degrees  rise  of  temperature. 
From  this  formula  we  have 


F  = 


c  x  w 


In  the  complete  combustion  of  one  pound  of  carbon,  for  in- 
stance, the-  products  are  3.66  pounds  of  carbonic  acid  and  8.63 
pounds  of  nitrogen :  the  specific  heat  of  carbonic  acid  is 
0,2164,  and  the  specific  heat  of  nitrogen  0.2440.  The  heat 
evolved  is  14,400  English  units. 


TRANSFER  OF  HEAT.  113 

The  quantity  F  will  then  be,  from  the  above  equation, 


14,400 

F  = 


3.66  x  0.2164  +  8.63  x  0.2440 


205.  Such  determinations,  however,  have  but  little  practical 
value  for  solid  combustibles,  because  the  residual  incandescent 
solid  gives  off  rapidly,  by  radiation,  heat  which  does  not  pass  off 
with  the  gases.  The  amounts  of  heat  thus  given  off  for  different 
solid  combustibles  in  parts  of  the  whole  heat  evolved  are  given 
by  Peelet  as  follows  : 

For  Coal 0.55 

Coke 0.55 

Wood 0.29 

Charcoal 0.55 

Peat 0.25 

Peat-charcoal 0.48 

Assuming  that  one-half  the  heat  evolved  by  burning  one 
pound  of  charcoal  is  given  off  by  radiation,  the  temperature  of  the 

4969° 
gases  found  as  above  would  be  -^ —  =  2484.5°  F. 

The  quantity  of  heat  radiated  from  an  incandescent  combus- 
tible depends  not  only  on  the  temperature  of  the  combustible, 
but  also  on  the  temperature  of  the  absorbent,  and  the  nature  of 
the  surfaces.  On  this  account  there  does  not  appear  to  be  suf- 
ficient ground  for  ascertaining  the  temperatures  of  furnaces,  or 
of  the  escaping  gases  by  this  process.  It  is  well  known  from 
common  observation  that  the  temperature  in  ordinary  furnaces 
is  greatly  increased  by  a  more  rapid  supply  of  air ;  so  that  the 
quantity  of  heat  evolved  in  a  given  time,  and  the  temperature, 
are  thus  increased. 

Chemical  action  is  promoted  by  high  temperatures,  and  the 
conditions  for  increase  of  temperature,  increase  of  heat  evolved 
in  a  given  time,  and  rapidity  of  chemical  action,  are  coincident. 
Where  excessively  high  temperatures  are  desirable,  as  in  blast- 
furnaces, and  in  melting  metals,  the  substance  to  be  melted  is- 


TRANSFER   OF  HEAT. 

placed  in  contact  with  the  fuel,  and  all  external  radiation  pre- 
vented. Under  these  circumstances  air  may  be  supplied  in 
large  quantities  by  artificial  draft  to  the  combustible. 

In  open  furnaces,  however,  where  a  part  of  the  heat  is  to  be 
transferred  by  external  radiation  as  the  combustion  proceeds, 
too  much  air  may  be  hurtful  by  chilling  the  combustible  and 
diminishing  the  activity  of  the  fire.  In  all  cases,  complete  or 
perfect  combustion  requires  a  fixed  quantity  of  air,  any  ex- 
cess being  hurtful.  The  quantity  supplied  in  a  unit  of  time 
must  depend  on  the  surface  of  the  combustible  exposed  to  in- 
candescence or  inflammation,  and  the  rapidity  of  combustion. 

Actual  observation  by  a  thermometer  is  therefore  the  only 
reliable  means  of  ascertaining  the  temperatures  which  accom- 
pany combustion.  Such  observations,  for  high  temperatures,  are 
uncertain  and  unreliable  with  any  thermometer  now  known. 

In  many  applications  of  heat,  in  the  arts,  an  exact  knowledge 
of  the  high  temperatures  employed  would  be  of  great  value, 
and  a  reliable  high-temperature  thermometer  is  greatly  needed. 

206.  Application  of  the  Principles  of  Transfer  of  Heat  to 
Steam-Boilers. — The  quantity  of  water  which  a  steam-boiler 
will  evaporate  in  a  given  time  depends,  primarily,  on  the  tem- 
peratures to  which  those  parts  of  the  plates  of  the  boiler  known 
as  heating  surfaces  are  exposed,  and  to  the  extent  of  those  sur- 
faces. In  the  furnace,  the  crown  and  side-walls  are  exposed  to 
the  radiant  heat  of  the  incandescent  fuel,  and  to  the  contact  of 
the  heated  gases.  The  heating  surfaces  of  the  flues  are  usually 
exposed  to  the  contact  of  the  heated  gases  alone. 

The  temperature  of  the  fuel,  and  the  initial  temperature  of 
the  heated  gases,  depend  on  the  intensity  of  combustion,  or  the 
quantity  of  fuel  burned  on  each  square  foot  of  the  grate-surface 
in  a  unit  of  time,  and  also  on  the  kind  of  combustion  that  takes 
place  :  perfect  combustion,  in  this  connection,  designating  that 
in  which  no  combustible  gases  or  uncombined  oxygen  escape 
to  the  chimney.  For  the  transfer  of  heat  in  the  furnace  by 
radiation,  if  G  represent  the  number  of  square  feet  of  grate- 
surface,  and  q  the  quantity  of  heat  emitted  from  each  square 
foot  in  a  unit  of  time,  the  quantity  of  heat  transferred,  accord- 
ing to  the  laws  of  Dulong  and  Petit,  will  be,  in  algebraic  sym- 
bols, 

Q!  =  q  G  =  c  a   (a  '  —  1) 
or,  Ql  =  o,  (a*1  -  1) 


TRANSFER   OF  HEAT.  115 

The  transfer  of  heat  by  contact  of  the  heated  gases  in  the 
furnace  will  be  represented  by 

Q2  =  F  C2  ti1'233 

in  which  F  represents  the  total  furnace  surface,  and  the  total 
transfer  of  heat  in  the  furnace  will  be  — 

Qi  +  Q2  =  G!  (atj  -  1)  +  F  C2  t^233 

In  this  expression,  t^  represents  the  difference  between  the 
temperature  of  the  incandescent  fuel  and  the  temperature  of 
the  water  in  the  boiler.  If  tw  represent  the  temperature  of  the 
water  in  the  boiler,  the  temperature  of  the  gases  as  they  enter 
the  flues  will  be  tt  4-  tw.  From  this  initial  point,  the  temperature 
of  the  gases  will  diminish  until  they  leave  the  heating  surfaces 
in  their  course  to  the  chimney.  The  law  of  this  diminution  may 
be  thus  found:  Let  ql  represent  the  quantity  of  heat  transferred 
at  any  point  of  the  heating  surface  through  one  square  f  oot,  in 
one  unit  of  time,  the  difference  of  temperature  at  that  point 
being  t.  The  quantity  transferred  through  an  element  or  band 
of  the  heating  surface  represented  by  ds  will  be  q^s. 

The  reduction  of  temperature  which  the  gases  undergo,  in  a 
unit  of  time,  in  passing  that  surface,  will  be  dt,  and  the  quantity 
of  heat  lost  by  the  gases  will  be  represented  by  cwdt,  c  re- 
presenting the  specific  heat  of  the  gases,  and  w  the  weight  of 
gas  which  passes  the  element  ds  in  a  unit  of  time.  The  quantity 
of  heat  transferred  to  the  water  must  be  equal  to  that  lost  by 
the  gases,  and  hence  we  have  — 

qLds  —  c  w   dt 
c  w  dt 


Substituting  for  q  its  value  as  given  by  the  laws  of  Dulong  and 
Petit,  we  have  — 

c  w  dt 


Integrating  this  expression  between  the  limits  t1?  the  initial 


116  TRANSFER  OF  HEAT. 

temperature,  ta  the  temperature  of  the  gases  as  they  leave  the 
flues,  we  have 

-.233       -.233 


- 


(-. 
tt 


-  .233  c2 
from  which  the  value  of  ta  may  be  found. 


/ 

~~~  \ 


c  w  t,-888 


w  -  .233  c2   s   t2- 

In  this  expression  s  represents  the  whole  heating-surface  of  the 
boiler. 

This  expression  is  of  no  special  practical  value,  but  serves  to 
indicate  a  mode  by  which  the  initial  temperatures  may  be  found. 
The  temperature  t2  of  the  gases  as  they  leave  the  flues  may  usu- 
ally be  observed  by  a  common  thermometer,  and  it  would  only 
be  necessary  to  make  experiments  for  ascertaining  the  value  of 
w,  and  the  constants  which  enter  the  equation. 

If  the  initial  temperature  could  be  observed,  or  calculated 
with  certainty,  the  quantity  of  heat  imparted  to  the  water 
through  the  heating  surfaces  of  the  flues  might  be  found,  being 
represented  by 

Q3  =  c  w  (t,  -  t2) 

If  the  expression  d  s  =  -     1838    be  integrated  between  the 

c2t  • 

limits  tj  and  0,  which  supposes  that  the  flues  extend  far  enough 
to  reduce  the  temperature  of  the  gases  to  the  same  temperature 
as  the  water,  we  should  obtain  equations  by  which  the  relations 
between  q  and  s,  and  t  and  s,  become  known,  viz.  : 


c3  and  c4  being  constants,  and  s  being  expressed  in  units  of 
length  of  the  flues,  one  unit  being  the  length  which  corresponds 
to  a  segment  or  band  of  the  flue  which  is  equal  to  one  square 
unit  of  area. 

The  corresponding  formulas,  if  we  assume  with  Rankine  that 
q  =  A  ta,  will  be 


TKANSFER  OF  HEAT. 


117 


These  formulas  show  that  after  the  gases  enter  the  flues  the 
temperatures  diminish  very  rapidly,  and  that  the  quantity  of 
heat  transferred  through  each  square  foot  of  surface  diminishes 
by  one  formula  as  the  fifth  power,  and  by  the  other  as  the 
square,  if  the  distance  from  the  initial  point  increases. 

The  relative  efficiency  of  heating-surfaces  in  passing  towards 
the  chimney  may  thus  be  estimated. 

Increase  of  heating-surface  should  thus  be  made  as  near  to 
the  furnace  as  possible,  and  not  by  adding  length  at  the  extreme 
end  towards  the  chimney.  This  is  equivalent  to  diminishing 
the  unit  by  which  s  is  measured  in  the  preceding  formulas 
rather  than  to  increase  the  number  of  larger  units. 


L  I  ii  ix  A  R  L 

UNIVERSITY   OF 

..CALIFORNIA. 


CHAPTEK   Y. 

STEAM  GENERATORS. 

207.  To  whatever  use  heat  is  to  be  applied  through  the 
medium  of  steam,  the  apparatus  for  generating  and  retaining 
the  steam  is  constructed  on  the  same  general  principles  for 
all  purposes,  and  is  popularly  termed  a  BOILEE. 

It  may  be  described  in  general  terms  as  a  closed  metallic 
vessel,  kept  partly  filled  with  water,  with  arrangements  for 
imparting  heat  to  the  water  by  means  of  the  combustion  of  fuel. 

The  steam  generated  is  confined  in  the  vessel,  above  the 
water,  until  it  is  required  for  use,  when  it  is  drawn  off  through 
pipes. 

If  the  steam  is  required  as  a  source  of  power,  it  is  supplied 
to  another  apparatus,  called  the  steam-engine^  to  which  the 
fiow  of  steam  from  the  boiler  is  controlled  by  automatic  me- 
chanism. 

If  the  heat  of  the  steam  be  required  for  other  purposes,  such 
as  warming  apartments,  or  for  heating  liquids  or  other  bodies, 
the  flow  is  generally  regulated  by  hand,  or  is  dependent  on  the 
condensation  of  the  steam  at  the  point  at  which  it  is  utilized. 

This  metallic  vessel,  with  its  compartments  and  openings, 
takes  the  name  of  boiler  in  the  shops  where  it  is  manufactured. 
But  in  many  classes  or  forms  of  boilers  the  steam-generating 
apparatus  is  not  complete  until  the  boiler  is  set  up  in  brick- 
work, with  an  external  furnace  constructed  for  the  combustion 
of  the  fuel,  and  external  flues  made  for  conducting  the  heated 
gases  to  the  chimney  along  the  sides  of  the  boiler. 

In  others  the  boiler  is  ready  for  use  as  it  comes  from  the 
manufacturer,  having  within  its  external  shell  all  these  neces- 
sary arrangements  for  combustion  and  draft.  In  all  cases  cer- 
tain adjuncts  and  appurtenances  are  necessary,  such  as  the 
feed-pump  or  other  means  of  supplying  water,  with  the  neces- 
sary pipes  and  attachments,  the  safety-valve,  the  steam  and 
water  gauges,  and  grate-bars  for  the  furnace.  So  that  a  com- 


STEAM  GENERATORS.  119 

plete  steam-generating  apparatus  requires  something  more  than 
the  simple  vessel  which  constitutes  its  principal  and  important 
feature.  For  the  mere  exhibition  of  the  principal  phenomena 
connected  with  the  gene  ratio  a  of  steam,  such  a  vessel  of  the 
most  simple  form  and  construction  might  be  sufficient. 

But,  connected  with  its  uses  as  an  instrument  of  industrial 
economy  in  constant  use  throughout  the  world,  its  employment 
the  basis  011  which  rest  the  most  important  interests  of  civiliza- 
tion at  the  present  day,  and  its  construction  and  applications 
consuming  costly  materials,  it  has  become  an  object  deserving 
and  requiring  the  most  thorough  and  critical  study. 

208.  As  the  most  important  and  universal  use  to  which 
steam  is  applied  is  the  production  of  power,  the  primary  con- 
ditions which  steam  generators  should  fulfil  are  : 

1.  Strength  to  sustain  the  internal  pressures  to  which  they 
will  be  subjected. 

2.  Durability. 

3.  Economy,  or  efficiency,  in  evaporating  qualities. 

4.  Economy  of  construction  in  materials  and  workmanship. 

5.  Adaptation  to  the  particular  circumstances  of  their  use. 

6.  To  these  conditions  must  he  added  safety,  which  depends 
on  form,  construction,  strength,  and  qualities  of  materials,  as 
well  as  upon  management* 

The  first  condition — strength  to  sustain  the  internal  pressures 
— requires  the  consideration  of  the  materials  to  be  employed,  the 
statical  pressures,  or  strains,  to  which  these  materials  will  be 
subjected,  and  the  proper  forms  and  devices  to  resist  those 
strains. 

The  condition  of  durability  involves  the  action  of  these  ma- 
terials, and  their  preservation  under  the  varying  influences  of 
heat,  pressure,  and  the  chemical  reactions  to  which  they  will  be 
subjected  in  use. 

Economy  in  evaporative  qualities  calls  for  such  arrangements 
for  the  combustion  of  fuel  and  the  transfer  of  heat  as  shall 
utilize  the  greatest  possible  proportion  of  the  heat  which  is 
evolved  by  the  combustion  of  the  fuel. 

Economy  in  materials  and  construction  requires  the  employ- 
ment o£  the  least  amount  of  costly  materials,  and  the  least  labor 
in  the  construction,  that  shall  be  consistent  with  the  other  con- 
ditions. 

Adaptation  to  various  uses  gives  rise  to  various  forms,  in 


120  STEAM  GENERATORS. 

which  the  special  use  controls,  or  modifies  to  some  extent,  some 
of  the  other  conditions ;  while  safety  of  life  and  property  de- 
mands that  strength  of  parts,  quality  of  materials,  excellence  of 
workmanship,  and  skilful  management  shall  not  only  meet  the 
requirements  of  economy,  durability,  and  adaptation,  but  shall 
place  beyond  contingencies,  as  far  as  possible,  the  occurrence 
of  explosions. 

As  far  as  they  relate  to  construction  alone,  the  conditions  of 
economy  and  safety  stand,  to  a  certain  extent,  in  constant  an- 
tagonism :  the  least  amount  of  material  that  will  bear  the  inter- 
nal pressures  being  the  extreme  limit  of  economy  of  construc- 
tion, while  a  near  approach  to  this  limit  is  always  attended  by 
excessive  risk.  But  as  true  economy  includes  permanence  and 
durability  under  continuous  use,  it  may  be  said  that  all  the 
essential  conditions  are  involved  in  strength,  economy  of  con- 
struction and  use,  durability,  and  adaptation. 

209.  These  considerations,  applied  in  practice,  with  the  aid  of 
experiments  on  the  resistance  of  materials,  and  a  knowledge  of 
the  principles  of  mechanics,  the  laws  of  heat,  the  chemical  pro- 
cesses of  combustion,  and  the  action  of  bodies  under  the  influ- 
ences of  heat,  have  led  to  certain  general  rules  and  principles 
which  to  a  certain  extent  have  been  reduced  to  form  and  are 
general  in  their  application. 

In  some  important  features  of  construction  and  use,  how- 
ever, there  exists  still  a  deficiency  in  regard  to  definite  rules  of 
practice  which  may  be  universally  applied,  and  engineers  and 
manufacturers  of  boilers  are  often  governed  solely,  in  some  of 
the  details  of  construction,  by  precedents  or  observations  de- 
rived from  their  individual  experiences. 

The  laws  which  govern  the  selection  of  materials,  the  resist- 
ance of  materials  to  rupture,  the  forms  of  construction  best 
suited  to  sustain  strains  and  involving  the  least  material,  the 
laws  which  determine  the  amount  of  the  strains  which  arise 
from  the  elastic  force  of  steam  under  different  temperatures, 
and  the  properties  of  water  and  steam  under  changes  of  heat, 
are  .sufficiently  well  determined. 

On  the  other  hand,  the  determination  of  the  proper  dimen- 
sions and  relative  proportions  of  parts  of  steam  generators — 
such  as  the  grate-surface,  the  heating-surface,  the  draft  areas, 
and  the  cross-sections  and  heights  of  chimneys — which  shall 
give  the  most  economical  results  in  the  evaporation  of  water — 


STEAM  GENERATORS.  t      121 

can  hardly  be  said  to  have  been  reduced  to  exact  rules,  uni- 
versally accepted  and  practised. 

The  processes  of  combustion  and  transfer  of  heat,  and  the 
supply  of  air  to  the  furnaces,  are  subjects  which  do  not  admit, 
in  the  present  state  of  knowledge,  of  exact  and  positive  analysis, 
and  the  result  of  such  uncertainties  is  undoubtedly  to  cause  a 
great  loss  of  fuel  in  a  large  proportion  of  instances  in  current 
applications.  Experience  and  observation  under  different  con- 
ditions of  use  have  led,  however,  to  the  establishment  of  certain 
general  rules  for  dimensions  and  proportions,  which  serve  to 
estimate  the  performance  of  boilers  within  practicable  limits  ; 
and  although  these  rules  are  different  in  different  countries, 
and  often  in  different  shops  or  under  different  engineers,  yet 
when  the  dimensions  of  the  apparatus  are  such  as  to  produce  a 
surplus  of  steam  for  any  purpose,  the  regulation  of  the  quantity 
generated  and  the  economy  of  the  process  are  subject,  to  some 
extent,  to  the  control  of  the  engineer  or  stoker. 

210.  Forms  of  Boilers. — In  regard  to  forms  and  adaptation 
to  various  uses,  the  results  of  experience  have  been  more 
definite.  The  designs  or  forms  in  general  use  may  be  class- 
ified under  a  few  types,  which  serve  to  illustrate  not  only 
general  principles  of  construction,  but  the  adaptability  of  the 
various  forms  to  particular  circumstances  of  use. 

Considered  merely  in  reference  to  strength  and  internal 
capacity,  combined  witli  the  least  weight  of  material,  the 
spherical  form  is  that  which  fulfils  the  theoretical  requirements 
of  strength  and  safety.  This  is  the  form  which  a  gaseous  sub- 
stance, enclosed  by  an  elastic  envelope,  assumes  under  the 
opposing  effects  of  its  internal  elastic  force  and  a  uniform  ex- 
ternal resisting  pressure.  A  vessel  of  this  form  possesses  the 
advantage,  in  regard  to  strength,  that  every  point  of  the  shell 
or  external  envelope  is  exposed  to  a  strain  of  extension.  No 
cross-strain  is  produced  in  any  part  of  the  material,  and  no 
distortion  can  occur  from  the  internal  pressures. 

The  spherical  form  is  not,  however,  the  best  adapted  for  the 
application  of  heat  externally,  nor  is  it  the  form  of  cheapest 
construction.  Those  conditions  are  obtained  by  modifying  this 
form  and  extending  it  to  the  cylindrical  shape,  which  gives  the 
same  advantages  in  transforming  all  the  strains  into  tangential 
strains,  while  it  permits  of  the  most  extensive  variety  of  arrange- 
ments for  the  application  of  heat.  The  cylinder,  whether  it  be 


122  STEAM  GENERATORS. 

used  for  the  exterior  shell  of  the  boiler,  in  which  it  is  subjected 
to  internal  pressures,  or  for  the  flues  or  tubes  required  for  the 
flow  of  the  gases  to  the  chimney,  or  for  the  liquid  circulation, 
is  the  form  best  adapted  for  cheapness  of  construction,  strength, 
permanence  of  shape  under  both  internal  and  external  pressures, 
and  for  the  flow  of  fluids ;  and  it  thus  forms  a  basis  for  nearly 
all  constructions ;  modifications  or  departures  from  this  form 
being  adopted  only  in  exceptional  cases,  such  as  the  boilers  of 
steam-vessels,  where  the  figure  of  the  external  shell  is  often 
adapted  to  the  position  and  space  available. 

211.  The  various  types  of  steam-generators  may  be  arranged 
under  the  following  designations : 

1.  The  Plain  Cylinder  13 oiler. 

2.  The  Cylinder-Flue  Boiler. 

3.  TJiB  Cylinder-Tubular  Boiler. 
4c.  The  Return-Flue  Boiler. 

5.  The  It  eturn- Tubular  Boiler. 

6.  The  Water- Tube  Boiler. 
1.  The  Locomotive  Boiler. 
8.  The  Sectional  Boiler. 

Each  of  these  types  appears  under  various  forms,  and  the 
modifications  often  present  such  peculiar  and  distinct  character- 
istics that  they  would  scarcely  be  classed  with  either  of  the  above- 
named  types.  But  for  a  general  discussion  these  forms  com- 
prehend the  largest  proportion  of  boilers  at  present  in  use,  or 
which  have  been  in  use  during  the  last  quarter  of  a  century. 

212.  The  Plain  Cylinder  Boiler,  represented  as  it  comes 
from  the  manufacturer's  hands  in  Plate  I.,  page  122*,  is  a  plain 
cylinder,  formed  of  wrought-iron  plates  of  -f^  to  J  inch  thick- 
ness, according  to  the  size  of  the  boiler,  the  ends  of  the  cylinder 
being  closed  by  cast-iron  heads,  or  by  wrought-iron  plates  ham- 
mered into  the  form  of  a  segment  of  a  sphere.     The  plates 
forming  the  body  of  the  cylinder  are  shaped  to  a  cylindrical 
form  in  a  cold  state  by  rollers,  the  sections  thus  formed  being 
riveted  together  longitudinally,  and  afterwards  joined  end  to  end. 

The  cylinder  is  surmounted  at  some  point  by  a  cylindrical 
chamber,  called  the  steam-dome,  or  steam-drum,  which  is  closed 
at  the  top  by  a  cast  or  wrought  iron  head,  on  which  the  castings 
for  attaching  the  steam-pipes  and  the  safety-valve  are  usually 
fitted. 

This  cylindrical  structure  is  called  in  the  shops  a  boiler,  but 


STEAM  GENERATORS. 


122^ 


123* 


STEAM  GENERATORS. 


/v  / 

'j 

^K      * 

STEAM  GENERATORS.  (  ,  ^1^3 

\^^^    *  '  y    /  ' 

the  complete  apparatus  to  which  this  term  appropria^ebp  Be- 
longs requires  other  parts,  which,  for  this  class  of  boilers,  itf  \* 
usually  supplied  by   the  brick-work  setting  in   which  it   is 
mounted. 

Plate  II.,  page  123"*,  represents  a  cylinder  boiler  set  in  brick- 
work. The  front  end  of  the  cylinder  rests  upon  a  cast-iron 
frame,  called  the  Front,  shown  in  section,  and  partly  in  the  end 
elevation  of  the  figure. 

The  rear  end  of  the  cylinder  rests  upon  a  brick  wall,  a  roller 
being  placed  under  this  end  to  permit  a  slight  movement  when 
the  cylinder  expands  or  contracts,  the  object  being  to  prevent 
the  shattering  or  breaking  of  the  walls  by  the  expansions  and 
contractions  when  the  boiler  is  alternately  heated  and  cooled. 

The  setting  of  a  boiler  of  this  character  consists  usually  of  a 
chamber  formed  by  the  iron  boiler-front,  two  side  walls,  and  a 
rear  closing  wall  of  brick.  The  side  walls  are  built  up  parallel 
to  each  other,  as  shown  in  the  longitudinal  section  and  end 
view,  Plate  II.,  at  a  distance  from  each  other  a  little  greater 
than  the  diameter  of  the  shell  of  the  boiler.  These  walls  are 
held  together  by  clamps,  (b uck-staves\  connected  at  the  top  and 
bottom  by  long  bolts,  as  shown  at  B  in  the  end  view. 

The  space  underneath  the  boiler-shell  is  divided  into  two 
portions  by  a  wall  called  the  bridge-wall.  The  chamber  in 
front  of  the  bridge- wall  is  devoted  to  the  combustion  of  the 
fuel,  and  is  called  the  furnace-chamber.  This  chamber  is 
divided  by  the  grate  into  two  chambers,  the  upper  being  the 
furnace  .and  the  lower  the  ash-pit.  The  upper  part  of  the 
bridge-wall  extends  nearly  to  the  shell  of  the  boiler,  the  top 
being  finished  in  a  cylindrical  form,  as  shown  at  F  in  the  end 
view,  Plate  II.  This  upper  portion  is  called  the  bridge.  It  is 
usually  made  of  fire-bricks,  and  its  office  is  twof old :  to  furnish 
a  rear  wall  to  the  furnace,  and  to  contract  the  entrance  to  the 
flue  to  the  area  proper  or  suitable  for  the  most  efficient  draft. 

The  chamber  in  rear  of  the  -bridge-wall  is  contracted  into  a 
flue  by  solid  filling  up  nearly  to  the  surface  of  the  cylinder. 
This  flue,  formed  by  the  solid  bottom,  the  side  walls  of  the 
boiler,  and  the  lower  half  of  the  cylindrical  shell,  serves  the 
purpose  of  conducting  the  products  of  combustion  to  the  chim- 
ney, and  also  for  the  transfer  of  the  heat  of  these  gases  to  the 
water  in  the  boiler  through  the  shell.  Arches  are  turned 
inwardly  from  the  side  walls  to  meet  the  shell  at  about  the 


124:  STEAM  GENERATORS. 

extremities  of  the  horizontal  diameters  of  the  shell,  and  the  flue 
thus  constructed  has  the  shape  shown  above  F  in  the  end  view, 
Plate  II. 

The  furnace  F  extends  from  the  front  back  to  the  bridge- 
wall.  In  this  class  of  boilers  the  width  of  the  furnace  is  gen- 
erally equal  to  the  distance  between  the  side  walls,  and  the 
depth  or  distance  from  the  front  to  the  bridge  is  determined 
by  the  conveniences  of  firing,  being  usually  from  four  to  seven 
feet. 

The  main  flue  underneath  the  boiler  terminates  in  a  cham- 
ber, C,  Plate  II.,  which  is  connected  with  the  bottom  of  the 
chimney.  This  chamber  takes  the  general  name  of  connection, 
or  smoke-connection.  The  chimney  may  be  connected  with 
the  smoke-connection,  or  chamber,  directly,  or  it  may  be  isolated 
and  connected  through  another  flue  or  conduit. 

The  chimney  is  a  vertical  flue,  the  object  of  which  is  usually 
twofold,  viz. :  1st,  to  cause  a  draft  or  supply  of  air  through  the 
furnace,  in  which  its  functions  are  those  of  a  machine  operated 
by  the  heat  of  the  gases  ;  and  2d,  to  carry  off  the  products  of 
combustion  beyond  hurtful  or  disagreeable  proximity. 

The  principal  parts  of  the  plain  cylinder  boiler,  which  are 
also  represented  wholly,  or  in  part,  in  nearly  all  boilers  under 
the  same  names,  are — 

1.  The  shell,  or  external  envelope. 

2.  The  furnace,  F ;  the  chamber  in  which  combustion  takes 
place. 

3.  The  flue,  or  flues  ;  the  passages  for  the  heated  gases  to  the 
chimney. 

4.  The  bridge,  or  rear  wall  of  the  furnace,  which  forms,  with 
the  shell  of  the  boiler  above  it,  the  boundary  of  the  draft-area. 

5.  The  ash-pit;  the   bottom  part  of  the  furnace-chamber, 
which  serves  as  a  receptacle  for  the  ashes  and  cinders,  and  also 
as  an  entrance  for  air  underneath  the  grate. 

6.  The  grate,  which  is  composed  of  grate-bars,  or  fire-bars, 
forming  the  bottom  of  the  furnace  on  which  the  fuel  is  laid. 

7.  The  furnace  door. 

8.  The  ash-pit  door. 

9.  The  combustion  chamber.     This  is  an  enlargement  of  the 
main  flue  in  rear  of  the  bridge,  formed  by  dropping  the  bottom 
of  this  flue  a  few  inches.     This  part  of  the  main  flue  is  often 
called  the  combustion  chamber,  under  the  assumption  that  the 


STEAM  GENERATORS.  125 

combustion  of  the  volatile  portions  of  the  fuel  is  not  completed 
in  the  furnace,  and  that  an  enlargement  of  this  flue  into  a  sort 
of  chamber  favors  a  more  thorough  mixing  of  the  air  and  the 
volatile  or  combustible  gases,  and  thus  produces  complete 
combustion.  This  is  perhaps  true  where  air  is  admitted  by 
a  special  arrangement  behind  the  bridge,  or  through  holes  in 
the  furnace  door.  When  bituminous  coal,  or  fuel  containing 
a  large  quantity  of  volatile  matter,  is  used,  some  such  arrange- 
ment for  burning  the  volatile  matters  should  be  made. 

10.  The  smoke-box,  or  smoke-connection,  is  more  important 
in  some  other  classes  of  boilers  than  in  the  plain  cylinder  boiler, 
as  will  appear  in  the  description  of  those  boilers. 

11.  The  steam-dome  is  a  vertical  chamber  set  upon  the  upper 
surface  of  the  shell,  and  communicating  with  it  freely  through 
holes  in  the  shell,  or  through  a  single  large  aperture,  the  object 
of  which  is  to  furnish  a  chamber  for  the  steam  above  the  steam- 
space,  in  which  the  steam,  being  removed  as  far  as  possible 
from  the  liquid  water  in  the  boiler,  and  being  in  a  quiescent- 
state,  any  particles  of  water  which  are  carried  up  with  the 
steam  may  be  separated  by  precipitation. 

In  some  boilers,  especially  those  for  marine  purposes,  this 
dome  takes  the  form  of  an  annular  space,  which  is  traversed 
by  the  smoke-stack  or  chimney,  and  is  then  called  the  steam- 
chimney. 

12.  Water-room  and  steam-room.     The  interior  of  the  shell 
of  the  boiler  is  divided  by  the  surface  of  the  water  in  to  two 
spaces,  called  the  water-room  and  steam-room,  or  water-space 
and  steam-space  ;  all  the  space  occupied  by  water  below  the 
water-level   being  water-space,  and  the  space  or  spaces  above 
the  water-level,  including  the  steam-dome,  being  steam-room. 

The  water-room  of  a  plain  cylinder  boiler  occupies  about  f 
of  the  whole  space,  and  generally  in  other  boilers  about  f  of 
the  internal  capacity  of  the  shell  when  the  water  is  at  its  mean 
level. 

13.  Man-holes,  hand-holes.     It  is  important  in  the  manage- 
ment of  boilers  to  examine  all  accessible  parts  frequently  ;  and 
accessibility  to  every  part  is  a  fundamental  principle  of  con- 
struction, not  only  for  cleaning,  but  for  facilitating  repairs. 
Man-holes  are  apertures  left  in  the  shell,  and  closed  by  strong 
plates  which  can  be  removed  at  will,  the  opening  being  large 
enough  to  admit  a  man.     Hand-holes  are  smaller  openings, 


126  STEAM  GENERATORS. 

generally  near  the  bottom,  which  answer  the  purpose  of  clean- 
ing by  means  of  tools. 

14.  Heating-surface.       In  all  boilers  portions  of  the  iron 
plates,  which  form  the  shell,  flues  or  tubes,  are  exposed  on  one 
side  to  the  heat  of  the  furnace,  or  the  heat  of  the  gases  in  their 
course  to  the  chimney,  and  on  the  other  side  to  the  contact  of 
the  water  or  steam,  the  transfer  of  heat  being  from  the  furnace 
and  -flues  to  the  water  through  these  portions  of  the  iron  struc- 
ture.    A.  heating -surf ace  in  a  steam  generator  may  therefore 
be  defined  to  ~be  any  surface,  which  acts  as  a  medium  for  the 
transfer  of  heat  from  the  furnace  or  gases  to  the  water  or 
steam  within  the  boiler.     The  efficiency  of  such  a  surface  de- 
pends, according  to  the  principles  which  have  been  enunciated 
in  the  chapter  on  transfer  of  heat,  on  the  difference  between  the 
temperatures  of  the  furnace  or  gases  and  the  water,  and  the 
thorough  and  rapid  circulation  of  the  fluids  and  gases  in  con- 
tact with  the  surfaces. 

Several  adjuncts  or  appurtenances  are  needed  to  give  effi- 
ciency and  safety  to  the  boiler,  viz. : 

15.  The  feed  apparatus,  which  is  composed  of  a  pump,  an 
injector,  or  other  device,  with  the  necessary  pipes  for  supplying 
water  to  the  boiler. 

16.  The  safety-valve.     A  valve  opening  outwards,  and  so 
adjusted  and  arranged  that  it  will  be  opened  by  the  internal 
pressure  of  the   steam,  when  that  pressure  exceeds  a  given 
amount  per  square  inch. 

17.  The  steam-gauge.     An  instrument  which  exhibits  at  all 
times  to  the  eye  of  the  engineer  or  stoker  the  pressure  of  the 
steam  in  the  boiler. 

18.  Water-gauges,  and  gauge-cocks,  which  are  intended   to 
show  at  any  instant  the  level  of  the  water  within  the  boiler. 

19.  The  low-water  detector.      An  instrument   attached    to 
many  boilers,  by  means  of  which  an  alarm  is  given  if  the 
water  falls  below  a  given  point. 

To  these  "fittings,"  as  they  are  sometimes  called,  may  be 
added  also  the  necessary  stoker's  tools  for  feeding  and  manag- 
ing the  furnace,  cleaning  the  flues  and  tubes,  and  removing 
ashes  and  clinker. 

These  descriptions  of  the  various  parts  are  applicable  to  all 
Bteam-generators,  and,  though  variously  modified,  perform  the 
same  offices  in  all.  A  repetition  of  the  descriptions  will  therefore 


STEAM  GENERATORS. 


STEAM  GENERATORS.  127 

be  unnecessary  in  referring  to  other  kinds  of  boilers,  a  reference 
to  the  plates  being  sufficient  to  show  the  special  combinations 
in  each  case. 

The  plain  cylinder  boiler,  which  has  been  described,  is  the 
most  simple  in  construction  of  all  boilers,  and  for  this  reason  it 
is  employed  where  economy  of  first  cost  is  desirable,  and  where 
economy  of  fuel  is  a  secondary  matter. 

The  furnaces  and  flues  are  external  to  the  shell.  The  heating- 
surface  comprises  all  of  the  lower  part  of  the  cylindrical  shell 
which  is  exposed  to  the  heat  of  the  furnaces  and  gases  ;  the 
amount  of  heating  being  estimated  algebraically  by  the  for- 
mula — 


s  = 

s  representing  the  heating-surface,  TT  the  number  3.1416,  D  the 
diameter,  and  L  the  length  of  the  shell.  These  boilers  usually 
range  from  18  inches  to  36  inches  in  diameter,  with  correspond- 
ing lengths  of  18  to  36  feet. 

For  the  usual  dimensions  employed  in  practice,  evaporative 
powers,  and  proportions  of  parts,  see  page  141. 

Plate  III.,  page  127*,  represents  two  sets  of  three  each  of 
such  boilers  ;  the  end  view  of  four  only  being  shown. 

These  boilers  were  made  by  the  Novelty  Iron  Works,  New 
York,  for  the  Acadia  Coal  Company  of  Nova  Scotia. 

The  boilers  are  each  34  inches  diameter  and  30  feet  long. 
The  grate-bars  5  feet  long.  The  steam-dome  20  by  36  inches. 
Height  from  bottom  of  ash-pit  to  central  line  of  boilers.  6  feet 
2  inches. 

Each  boiler  had  136  feet  of  heating-surface,  and  T6Q-  of  a 
cubic  foot  of  steam-space  for  each  square  foot  of  heating-sur- 
face. 

In  such  arrangements  as  those  shown  in  Plate  III.  the  steam- 
domes  are  connected  by  a  cross-pipe  of  large  dimensions,  in 
order  that  there  may  be  free  steam  communication  between  the 
separate  boilers. 

The  construction  and  mode  of  setting  of  the  plain  cylinder 
boiler  require  a  greater  length  for  a  given  amount  of  heating- 
surface  than  any  other  form  of  boiler,  and  on  account  of  the 
increased  expense  of  brick-work  setting,  when  the  length  is 
greatly  extended,  the  increased  room  necessary,  and  other  at- 


128  STEAM  GENERATORS. 

tendant  disadvantages,  economy  of  fuel  is  often  sacrificed  to 
economy  of  construction.  For  other  reasons,  also,  economy  of 
fuel  is  not  to  be  expected  in  this  form  of  boiler.  Its  advan- 
tages are  cheapness  of  construction,  facility  of  access  for  re- 
pairs, and  general  simplicity. 

213.  The  French  Boiler. — A  modification  of  the  plain  cyl- 
inder boiler,  called  in  England  the  FRENCH  BOILER,  and  also  the 
ELEPHANT  BOILER,  and  in  France  the  CHAUDIERE  A  BOUILLEURS, 
is  much  used  on  the  continent  of  Europe,  and  also  to  some  ex- 
tent in  England.  It  is  seldom  seen  in  this  country,  although  a 
boiler  involving  the  same  principal  features  is  often  constructed 
here  for  shipment  to  the  West  India  sugar  plantations.  A 
sketch  of  one  of  these  boilers  is  shown  in  Plate  IV.,  page  128*. 
This  boiler  consists  of  two  cylinders  of  equal  diameter,  one 
above  the  other,  connected  by  upright  cylinders  of  the  same 
diameter.  The  mode  of  setting  is  best  illustrated  by  Plate  V., 
page  128f,  which  represents  one  form  of  the  French  Boiler. 

Fig.  1?  Plate  Y.,  represents  a  longitudinal  and  Fig.  2  a  cross- 
section  of  this  boiler.  It  consists  of  one  large  cylinder,  with 
hemispherical  or  segmental  ends,  and  one,  two,  or  three  smaller 
cylinders,  about  half  the  diameter  of  the  larger,  connected  with 
the  larger  cylinder  by  two  or  more  vertical  cylinders.  The 
lower  cylinders  receive  in  France  the  name  "bouilleurs,"  while 
the  upper  or  larger  is  the  "  ehaudiere,"  or  boiler.  The  bou- 
illeurs, the  vertical  connecting  cylinders,  and  the  lower  half  of 
the  boiler  are  kept  filled  with  water.  The  course  of  the  flame 
and  gaseous  products  of  combustion,  when  there  are  two  bou- 
illeurs, or  heaters,  is  first  underneath  the  bouilleurs  from  the 
furnace  to  the  rear  end,  thence  back  through  a  side  flue  to  the 
front,  and  returning  to  the  rear  by  another  side  flue,  forming 
what  is  termed  a  "  wheel- draft." 

Within  the  same  length  the  amount  of  heating-surface  is  thus 
much  greater  than  in  the  simple  cylinder  boiler.  The  heating- 
surface  is  estimated  by  taking  the  total  external  surface  of  all 
the  bouilleurs,  or  heaters,  the  external  surface  of  the  vertical 
connecting  water-tubes,  and  half  the  surface  of  the  larger 
cylinder  or  boiler. 

Besides  the  advantage  of  increasing  the  extent  of  heating- 
surface  within  a  given  space,  this  boiler  possesses  other  special 
advantages  which  have  rendered  it  deservedly  popular  where 
it  has  been  most  used.  One  of  these  important  advantages 


STEAM  GENERATORS. 


128* 


STEAM  GENERATORS. 


128f 


STEAM  GENERATORS. 


STEAM  GENERATORS.  129 

is,  that  the  smaller  cylinders  only  are  exposed  to  the  initial 
temperatures  of  the  furnace  and  gases,  while  the  larger  are 
exposed  to  a  less  heat.  The  smaller  cylinders  can  thus  be 
easily  repaired  and  cleaned,  or  even  replaced,  and  as  the  larger 
cylinders  are  less  exposed  to  injury,  they  last  longer  than  the 
smaller  cylinders. 

According  to  Morin  and  Tresca,  two  bouilleurs  form  the 
most  convenient  and  efficient  arrangement,  though  one,  and 
three  are  often  employed. 

214.  Ot/Und#r-llbu&  Boiler.  —  This  modification  of  the  cylin- 
der boiler  is  characterized  by  an  arrangement  of  one  or  more 
internal  flues  of  large  diameter,  running  longitudinally  within 
the  shell  in  such  a  manner  that  the  heated  gases  pass  once 
through  these  flues,  and  once  through  one  or  more  flues  external 
to  the  shell. 

Plate  YL,  page  129*,  represents  the  shell  and  internal  flues 
of  one  of  these  boilers  as  it  comes  from  the  manufacturer's 
hands,  and  Plate  YI.  #,  a  set  of  two  cylinder-  flue  boilers  set 
in  brick-work. 

The  boilers  represented  by  Plate  YI.  $,  were  made  for  a 
high-pressure  engine,  by  the  Novelty  Iron  Works,  in  1866.  The 
length  of  the  shell  of  each  is  26  feet  ;  the  diameter,  4  feet  ; 
diameter  of  internal  flues,  16  inches  ;  length  of  grate-bars, 
4  feet  10  inches;  height  of  crown  of  furnace,  above  grate 
at  front  end  of  grate-bars,  2  feet  ;  dome,  24  x  30  inches  ;  heat- 
ing-surface, one-half  the  surface  of  the  shell  added  to  the  total 
surface  of  the  flues,  or, 


R  representing  the  radius  of  the  shell,  r  the  radius  of  the 
flues,  and  L  the  length  of  the  boiler. 

For  the  above-named  dimensions  the  total  heating-surface 
for  each  boiler  will  be  approximately  380  square  feet.  There 
is  approximately  80  cubic  feet  of  steam-room  in  each  boiler, 
and  17  square  feet  of  heating-surface  to  1  square  foot  of  grate- 
surface.  The  ash-pit  A,  the  furnace  F,  the  smoke-connection 
0,  the  water-space  W,  the  steam-space  S,  and  the  steam-dome 
D,  are  indicated,  as  in  all  the  other  plates,  by  these  letters 
respectively  ;  the  flues  or  conduits  for  the  flame  and  gases  to 
the  chimney  being  represented  by  the  black  shading,  and  the 
direction  by  the  arrows.  The  brick-work  setting  is  the  same 
9 


130  STEAM   GENERATORS. 

as  for  the  plain  cylinder  boiler.  In  this  class  of  boilers  the 
heated  gases  pass  underneath  the  shell  to  the  first  smoke-box 
or  connection,  and  return  through  the  internal  flues  to  the 
point  where  there  is  a  second  smoke-box  C',  from  which  the 
gases  are  led  by  a  side  fine,  made  of  light  iron,  to  the  chim- 
ney. Where  the  heated  gases  pass  from  one  flue  into  two  or 
more,  or  from  one  set  of  flues  or  tubes,  by  a  return,  to  another 
set,  the  smoke-connection  serves  to  equalize  the  draft  in  all 
the  flues  or  tubes,  and  should  be  arranged  with  this  view. 

Plate  YIL,  page  130*,  gives  a  longitudinal  section  and  an 
end  elevation  of  a  single  cylinder-flue  boiler,  mounted  in  brick- 
work, made  in  1863  :  length,  24  feet  8  inches ;  diameter,  42 
inches  ;  steam-dome,  24  inches  diameter  ;  grate-bars,  4  feet  10 
inches  long  ;  width  of  furnace,  4  feet.  This  boiler  is  provided 
with  two  flues,  each  13  inches  in  diameter.  This  and  the  fol- 
lowing plate  are  introduced  to  show  the  different  modes  of 
constructing  the  cast-iron  boiler-fronts. 

Plate  YIIL,  page  130f,  represents  another  construction  of 
boiler-front  for  the  same  class  of  boiler.  In  this  example  there 
are  two  boilers,  side  by  side,  as  in  Plate  YI.  For  dimensions 
in  current  use,  proportion  of  parts,  and  evaporative  powers,  see 
page  141. 

215.  The  Cornish  Boiler. — This  is  a  variety  of  the  cylinder- 
flue  boiler  which  has  been  long  in  use  in  England  for  stationary 
engines.  It  differs-  from  the  American  boiler  of  the  same  class 
in  having  an  internal  furnace.  The  furnace,  or  furnaces,  are 
placed  within  the  front  end  of  a  large  flue,  which  extends 
through  the  boiler  from  the  front  to  the  rear  end. 

Plate  IX.,  page  130J,  represents  a  longitudinal  section  and 
sectional  elevation  of  the  Cornish  boiler.  The  bridge  is  built 
of  fire-bricks  within  the  large  flue,  and  the  heated  gases  pass 
directly  through  the  flue,  which  is  entirely  surrounded  by 
water,  to  the  rear  end.  Returning  by  a  split-draft  along  the 
sides  of  the  boiler,  the  gases  pass  a  third  time  along  the  whole 
length  of  the  boiler,  from  front  to  rear,  underneath  the  shell 
This  is  the  usual  arrangement  of  the  draft,  but  it  is  often 
varied.  The  diameter  of  the  flue  is  usually  about  fff  the 
diameter  of  the  shell  of  the  boiler.  The  crown  of  the  furnace, 
and  a  portion  of  the  flue  beyond  the  bridge,  are  sometimes  lined 
with  brick  to  prevent  too  rapid  cooling  of  the  flame  before  the 
combustion  of  the  gases  is  complete.  These  boilers  are  some- 


STEAM  GENERATORS. 


130* 


STEAM  GENERATORS. 


130f 


*/•'"/, 


/J> 


^  /Ah/ 
u& 


STEAM  GENERATORS. 


130J 


STEAM   GENERATORS.  131 

times  made  with  two  cylindrical  flues,  and  sometimes  with 
two  internal  furnaces  leading  into  a  single  flue. 

The  efficiency  of  these  boilers  is  about  the  same  as  that  of  the 
ordinary  American  form  first  described.  With  very  low  rates 
of  combustion  the  economic  efficiency  is  increased  to  9  to  10 
pounds  of  water  evaporated  for  each  pound  of  coal  burned — 
the  ordinary  evaporation  of  cylinder-flue  boilers  being  about 
8  pounds  of  water  evaporated  for  each  pound  of  coal, — the 
rate  of  combustion  being  about  10  to  12  pounds  of  coal  on  each 
square  foot  of  grate-surface  per  hour.  The  furnaces  of  the 
Double  Furnace  Cornish  boiler  are  usually  fired  alternately,  in 
order  to  procure  a  more  complete  combustion  of  the  volatile 
gases  in  each  furnace. 

The  principal  objection  to  the  Cornish  boiler  is  the  large 
diameter  of  the  flue  or  flues,  which  renders  them  liable  to  col- 
lapse, especially  at  the  high  pressures  employed  at  the  present 
day. 

216.  Cylinder-Tubular  Boiler. — Boilers  of  this  class  differ 
so  little  from  the  common  cylinder-flue  boiler  described  above, 
that  they  might  with  propriety  be  classed  with  them.  They  form, 
however,  the  basis  of  a  variety  of  modified  forms,  and  in  prac- 
tice there  is  a  difference  between  flues  and  tubes,  not  only 
in  mechanical  construction,  but  also  in  the  modes  of  connecting 
the  flues  and  tubes  with  the  end-plates  of  the  boilers,  of  which 
they  form  parts.  Flues  differ  from  tubes  in  being  generally  of 
larger  dimensions.  They  are  usually  constructed  of  metallic 
plates  rolled  into  the  cylindrical  form,  and  then  riveted 
together  as  in  the  construction  of  the  shell  of  the  plain  cylinder 
boiler.  Tubes,  on  the  other  hand,  are  usually  constructed  by 
lapping  and  welding  the  edges,  instead  of  riveting  them ; 
special  machines  being  used  for  this  purpose.  Tubes  thus  con- 
structed are  now  made  from  the  smallest  form  of  pipes  to  a 
diameter  of  6  and  8  inches. 

Flues  and  large  tubes  are  usually  attached  to  the  heads  or 
end-plates  by  stovepipe-riveted  joints  or  by  angle-iron  rings, 
while  tubes  of  the  smaller  diameters  are  usually  inserted  at  the 
ends  into  neatly  drilled  holes  in  the  tube  sheets  or  end-plates, 
and  the  end  of  the  tube  is  then  expanded,  by  a  special  tool 
called  the  tube  expander,  to  the  extreme  extent  practicable,  so 
that  the  external  surface  of  the  tube  at  the  joint  not  only 
closely  fits  the  hole,  biit  the  material  of  the  tube  is  expanded 


132  STEAM   GENERATORS. 

into  annular  welts  on  each  side  of  the  plate.  The  external 
edge  of  the  tube  is  then  turned  over,  or  calked,  by  another 
tool. 

Flues  may  always  be  regarded  as  conduits  for  heated  gases 
or  smoke,  while  tubes  may  conduct  gases  or  may  remain  filled 
with  water  and  act  as  passages  for  liquid  circulation,  while 
heated  gases  come  in  contact  with  their  external  surfaces  ;  in 
both  cases  acting  as  heating-surf  aces.  In  estimating  heating- 
surfaces  the  fire-surf  ace,  not  the  water-surface,  is  taken. 

Thus,  in  regard  to  size  or  diameter,  mechanical  construction, 
mode  of  attachment,  and  in  functions,  the  tube  may  differ  from 
the  flue. 

The  common  cylinder-tubular  boiler  is  in  every  respect 
similar  to  the  cylinder-flue  boiler,  except  that,  instead  of  large 
internal  return  flues,  there  are  many  returning  tubes,  and  the 
gases,  after  having  passed  through  the  main  external  flue  un- 
derneath the  boiler,  return  through  these  tubes  to  the  front, 
where  the  tubes  all  terminate  in  a  common  smoke-connection 
or  chamber.  All  the  parts,  and  the  mode  of  setting,  are  the 
same  as  for  the  cylinder-flue  boiler.  The  employment  of  tubes 
instead  of  large  flues  permits  of  a  still  further  diminution  of 
the  external  length  of  shell  for  the  same  amount  of  heating- 
surface,  and  permits  of  the  use  of  higher  pressures  of  steam 
with  greater  safety. 

This  form  of  boiler,  with  its  various  modifications,  is  proba- 
bly in  more  universal  use  at  the  present  day  than  any  other 
form  of  cylinder  boiler.  It  constitutes  the  basis  of  all  marine- 
tubular  boilers,  even  where  the  shell  is  not  cylindrical,  and  for 
stationary  engines  is  very  extensively  used. 

Plate  X.,  page  132*,  gives  a  longitudinal  and  cross-section  of 
the  shell  of  a  cylinder-tubular  boiler.  This  plate  represents  a 
boiler  of  the  following  dimensions :  Length,  14  feet ;  diameter, 
47  inches  ;  dome,  24  x  36  inches  ;  it  has  40  tubes  3^-  inches  out- 
side diameter. 

Plate  XI.,  page  132*,  represents  another  shell  of  this  char- 
acter: 16  feet  in  length  ;  51  inches  outside  diameter,  with 
32  4-inch  tubes.  This  boiler  was  built  for  a  manufacturing 
establishment  where  wood-shavings  constituted  the  fuel. 

Plates  XII.,  XIIL,  XIV.,  and  XV.,  pages  132f,  132;):,  132§, 
132||,  represent  cylinder-tubular  boilers  set  in  brick-work.  The 
sections  and  end  elevations  show  the  construction  of  the  walls, 


STEAM  GENERATORS. 


Fig.  2. 


Fig.  1. 


PLATE  X.— Shell  of  Cylinder-Tubular  Boiler. 


Fig.  2. 


Fig.  1. 


PLATE  XI.— Shell  of  Cylinder-Tubular  Boiler. 


STEAM  GENERATORS. 


132* 


L  I  jb 
|  UNIVERSITY -OF 

CALIFORNIA. 


PLATE  XII.— Cylinder-Tubular  Boiler  set  in  Brick-work. 


STEAM  GENERATORS. 


132$ 


STEAM  GENERATORS. 


132§ 


STEAM  GENERATORS. 


132J 


133* 


STEAM  GENERATORS. 


133f 


STEAM  GENERATORS. 


PLATE  XVII.— Return-Flue  Boiler. 


PLATE  XVIII. — Return-Flue  Boiler. 


133J 


STEAM  GENERATORS. 


133§ 


STEAM  GENERATORS. 


PLATE  XX.— Drop  Return-Flue  Boiler. 


STEAM  GENERATORS.  133 

the  furnace  and  flues,  the  arch  of  brick  covering  the  boiler, 
and  other  features  of  construction. 

Plate  XII.  page  132f,  represents  a  boiler  in  which  the  furnace- 
gases,  after  returning  through  the  tubes  to  the  front  of  the 
boiler,  pass  back  between  the  brick  arch  and  the  top  of  the 
boiler  to  the  chimney. 

Plate  XIII.,  page  132J,  represents  a  set  of  two  cylinder- 
tubular  boilers  mounted  together.  The  shells  of  these  boilers 
are  16  feet  in  length,  with  an  extension  of  the  water-space  in 
front  over  the  furnace  of  two  feet,  to  form  the  smoke-box  ; 
diameter  of  shell,  4  feet  ;  number  of  3-inch  tubes,  30  ;  dome, 
30x36  inches;  grate-bars  in  -double  length;  furnaces,  each  4 
feet  4  inches  wide  and  5  feet  deep  ;  height  of  crown  of  fur- 
nace above  grate,  26  inches.  The  bridge-walls  of  all  f  uriiaces 
set  in  brick-work  are  usually  12  inches  thick,  and  are  topped 
out  above  the  grate  with  fire-bricks.  The  domes  of  these  boil- 
ers are  connected  by  a  pipe  of  large  diameter,  in  which  is 
placed  a  stop-valve.  The  feed-pipes  are  shown  in  front  as  in 
other  examples. 

Plate  XIV.,  page  132§,  shows  a  pair  of  such  boilers  set  in 
brick-work,  the  domes  being  surrounded  by  brick-work.  This 
plate  exhibits  the  external  appearance  of  the  shell  as  it  is 
mounted. 

Plate  XV.,  page  132|,  represents  a  pair  of  boilers,  each  16 
feet  long  and  48  inches  diameter,  and  having  33  tubes,  each  4 
inches  diameter.  The  furnaces  in  this  boiler  are  each  5  feet  in 
depth,  and  4^  wide  ;  the  domes  24  inches  diameter. 

In  the  cylinder-tubular  boilers  the  heating-  surf  ace  is  found 
by  adding  to  half  the  external  surface  of  the  shell,  the  aggre- 
gate internal  surfaces  of  the  tubes,  and  is  represented  by  the 
following  formula  : 


in  which  s  represents  the  heating-surface  ;  B,  the  radius  of  the 
shell  ;  r,  the  internal  radius  of  the  tubes  ;  L,  the  length  of  the 
boiler,  and  n,  the  number  of  tubes. 

For  dimensions,  proportions,  and  evaporative  powers  of  these 
boilers,  see  page  141. 

217.  Plates  XVI.,  XVII.,  XVIII.,  XIX.,  and  XX.  represent 
varieties  of  a  class  of  boilers  which  are  known  as  Return-Flue 
Boilers.  They  were  at  one  time  in  very  general  use  in  steam- 
boats and  steamships  in  this  country,  and  are  still  employed  to 


134:  STEAM  GENERATORS.' 

a  considerable  extent.  They  are  characterized  by  having  in- 
ternal furnaces  and  internal  flues,  no  external  furnaces  or  brick- 
work being  attached  to  the  boilers.  Constructed  in  this  man- 
ner, they  are  ready  for  use  as  they  come  from  the  hands  of  the 
manufacturer. 

The  shell  in  these  boilers  is  made  sufficiently  large  to  receive 
within  it  the  direct  flues  from  the  furnace,  from  front  to  rear, 
and  also  the  return  flues ;  the  arrangements  being  as  exhibited 
in  the  several  plates.  Two  or  more  furnaces  may  be  arranged 
side  by  side,  as  in  Plates  XVL,  XVII.,  and  XIX.,  or  the 
furnaces  may  be  arranged  in  upper  and  lower  levels,  as  in  Plates 
XVIII.  and  XX. 

218.  Plate  XX.  represents  a  boiler  which  receives  the  name  of 
Drop  Return,  from  the  downward  course  of  the  flues  in  pass- 
ing from  the  furnaces  to  the  chimney. 

Boilers  of  this  class,  when  applied  to  marine  purposes,  instead 
of  a  steam-dome,  have  what  is  called  a  steam-chimney.  This 
is  always  at  one  end,  in  order  that  the  smoke-chimney  may 
pass  up  through  the  steam-chimney.  The  effect  of  this  is  to 
dry  and  slightly  superheat  the  steam  before  it  is  drawn  off  to 
the  engine. 

These  boilers  having  large  diameters,  it  is  necessary  to 
strengthen  the  various  parts  by  stays,  as  shown  in  Plate  XVI. 
Around  the  furnaces  the  plates  are  stayed  and  kept  in  position 
by  sockets  and  bolts,  the  sockets  acting  as  struts  and  the 
bolts  as  stays. 

219.  Plate  XIX.  represents  a  boiler  in  which  there  are  direct 
flues  and  return  tubes.     In  these  boilers  the  smoke-connections 
are  important.      They  not  only  serve   to   equalize  the  draft 
through  the  flues  and  tubes,  but  the  bounding-surfaces  perform 
to  some  extent  the  functions     of    heating-surfaces,    and    are 
generally  estimated  as  part  of  the  heating-surfaces. 

The  total  heating- surf  ace  in  these  boilers  is  found  by  adding 
together  the  interior  surface  of  the  furnace,  the  interior  surfaces 
of  the  direct  and  return  flues,  and  the  surfaces  of  the  smoke- 
connections.  No  general  formula  is  applicable,  but  the  com- 
putation is  readily  made  in  any  special  construction.  There  is 
often  a  combustion-chamber  in  boilers  of  this  class,  behind  the 
furnace,  which  is  separated  from  the  furnace  by  a  water-bridge. 
Water-bottoms  and  water-legs  were  formerly*  constructed,  the 
former  as  security  against  fire  ;  but  experience  has  shown  that, 


STEAM  GENERATORS.  135 

owing  to  a  want  of  circulation,  and  the  exposure  of  these  parts 
to  external  moisture,  they  soon  became  corroded  and  required 
frequent  repairs,  and  it  is  now  considered  best  to  confine  water 
only  to  the  spaces  within  which  there  is  a  circulation,  and  to 
provide  security  against  fire  by  covering  the  floor  on  which  the 
boiler  rests  Avith  a  suitable  non-conducting  and  non-combusti- 
ble material.  The  following  are  the  dimensions  of  the  boilers 
represented  in  Plates  XVI.,  XVII.,  XVIIL,  and  XX.: 

Boiler  represented  in  Plate  XVI :  Length,  25  feet  over  all ; 
diameter  of  shell,  7  feet  6  inches;  diameter  of  direct  flues 
(five  to  each  furnace),  12,  12,  12,  9-J-,  8-J-  inches;  diameter 
of  return  flues,  8|-  inches ;  number  of  return  flues,  14 ;  depth 
of  grates,  7  feet ;  width  of  grates,  40f-  inches  ;  diameter  of  chim- 
ney, 56£  inches  ;  steam-chimney,  7  feet  9  inches  diameter,  12 
feet  high  ;  length  of  direct  flues,  11  feet  11  inches  ;  length  of 
return  flues,  18  feet  5  inches ;  first  combustion  chamber  behind 
the  bridge,  28  inches  deep ;  first  smoke-connection,  30  inches 
deep;  second  smoke-connection,  or  uptake,  40  inches  deep. 
This  boiler  was  built  for  the  steamer  Jesse  Hoyt,  a  side-wheel 
river  steamer,  in  May,  1867. 

Plate  XVIL,  a  boiler  built  for  the  ocean  steamer  Southerner. 
Length  over  all,  26  feet ;  length  of  direct  flues,  15  feet  6  inches ; 
diameter  of  direct  flues,  6  of  16  inches,  4  of  11  inches ;  return 
flues,  20  feet  3  inches  in  length,  16  inches  diameter;  shell  of 
boiler,  9  feet  diameter ;  depth  of  furnace,  7  feet  4  inches ; 
diameter  of  chimney,  3  feet;  diameter  of  steam-chimney,  5 
feet ;  height  of  steam-chimney,  9  feet  6  inches ;  height  of 
boiler  to  top  of  shell,  10  feet  3  inches.  This  boiler  belonged  to 
a  set  of  two,  each  of  which  had  58.76  square  feet  grate-surface; 
10.44  sq  uare  feet  fire-surface ;  area  of  cross-section  (draft  area) 
of  direct  flues,  7  square  feet;  return  flues,  11.6  square  feet; 
uptake,  7  feet ;  weight  of  each  boiler,  39,000  pounds ;  heating 
surface  of  each  boiler,  1044.6  square  feet. 
.  Plate  XVIII.  represents  one  of  two  boilers  built  for  the 
ocean  steamship  Nashville.  Whole  length,  24  feet ;  diameter 
of  shell,  12  feet  3  inches ;  length  of  direct  flues,  11  feet  8 
inches ;  return  flues,  18  feet  4  inches  ;  number  of  furnaces,  5  ; 
number  of  direct  flues  from  each  furnace,  3  ;  diameter  of 
direct  flues,  15  inches ;  diameter  of  return  flues,  13  and  11 
inches;  number  of  return  flues,  13  inches  diam.,  9;  number 
11  inches  diam.,  9 ;  diameter  of  chimney,  4  feet  10  inches ; 


136  STEAM  GENERATORS. 

diameter  of  steam-chimney,  7  feet  4  inches ;  height  of  steam- 
chimney  above  shell,  10  feet ;  grate-surface,  each  boiler,  150 
square  feet ;  heating  or  fire  surface,  each  boiler,  2,166  square 
feet ;  draft  area,  direct  flues,  18.4  square  feet ;  return  mies, 
13.7  ;  uptake,  18.3  square  feet. 

Plate  XX.  represents  one  of  the  boilers  of  the  steamship 
Arago,  formerly  running  between  New  York  and  Liverpool ; 
built  1855.  Whole  length,  29.3  feet;  flues,  16  feet  7  inches 
long,  and  13  inches  diameter ;  number  of  furnaces,  3  ;  num- 
ber of  direct  flues,  18  ;  number  on  first-drop  return,  18 ;  num- 
ber on  second-drop  return,  19  ;  aggregate  draft  area,  first  and 
second  sets,  16£  square  feet,  and  of  the  second,  17.7  square 
feet ;  diameter  of  chimney,  4  feet  9  inches  ;  diameter  of  steam- 
chimney,  7  feet  3  inches ;  smoke-connections,  21  inches  deep ; 
fire-surface  of  each  boiler,  4,320  square  feet ;  grate-surface, 
162  square  feet. 

220.  Marine  Tubular  Boiler.— Plate  XXI.,  page  136*,  repre- 
sents a  modification  of  the  return-tubular  boiler  suited  to  marine 
purposes.  The  limitation  of  space  in  the  hold  of  a  ship  ren- 
ders it  necessary  to  contract  the  boiler-space  as  much  as  possi- 
ble, and  the  form  of  boiler  adopted,  generally,  is  that  illus- 
trated in  Plate  XXI.  The  external  shell  receives  the  general 
form  of  which  Fig.  1  is  a  cross-section  and  Fig.  2  an  eleva- 
tion. The  arrangement  of 'the  furnaces,  flues,  tubes,  and  smoke- 
connections,  are  as  shown  in  the  figures.  In  boilers  of  this 
character,  each  boiler  contains  several  furnaces,  and  twro  or 
more  boilers  are  usually  set  together  on  opposite  sides  of  the  hold 
of  the  vessel,  in  such  a  manner  as  to  have  a  common  chimney. 

In  the  example  given  there  are  eight  furnaces  in  the  boiler. 
The  second  smoke-connection  runs  the  entire  length  of  the  boiler 
along  the  front  and  leads  to  the  chimney,  which  is  placed  near 
one  end.  The  boiler  represented  is  one  of  a  set  of  four  made 
for  the  side-wheel  steamship  Baltic.  The  peculiar  form  of  the 
shell  is  adapted  to  the  space  allotted  to  the  boiler  along  the  side 
of  the  ship's  hold,  as  is  usual  in  such  cases.  This  form  not  being 
cylindrical,  it  is  necessary  to  brace  all  flat  surfaces  which  receive 
pressure.  The  manner  in  which  this  is  accomplished  is  exhibited 
in  Fig.  4,  page  137*,  which  represents  the  bracing  of  the  boiler 
illustrated  in  Plate  XXI.  The  roof -plates  of  these  boilers  are 
sometimes  supported  by  iron  pillars  or  struts  extending  from  the 
roof  to  the  bottom,  between  the  furnaces. 


STEAM  GENERATORS. 


STEAM  GENERATORS. 


.  4. — Showing  the  mode  of  bracing  Mdrine  Tubular  Boilers. 


FIG.  6. — Grate-bars. 


137f 


STEAM  GENERATORS. 


STEAM  GENERATORS.  137 

The  amount  of  heating-surface  of  boilers  of  this  class  is  to  be 
estimated  according  to  the  general  principle  that  all  plates 
which  serve  to  transmit  heat  from  the  furnace,  or  from  the 
heated  gases,  to  the  water,  are  counted  as  heating-surfaces.  In 
the  boiler  under  discussion  this  includes  the  furnace,  the  tubes, 
and  the  front  and  back  connections. 

The  boiler  exhibited  in  Plate  XXI.  has  the  following  dimen- 
sions :  Shell,  27  feet  6  inches  long,  13  feet  6  inches  deep,  12  feet 
1  inch  high ;  number  of  furnaces,  8 ;  number  of  tubes,  704 ; 
length,  7  feet ;  diameter,  3  inches ;  total  heating-surface,  5,032 
feet;  aggregate  area  of  tubes,  29  sq.  feet;  grate-surface,  160 
square  feet ;  diameter  of  smoke-pipe,  11  feet. 

221.  Marine  Water-Tube  Boilers.— Plate  XXII.,  page 
137f,  exhibits  a  construction  which  differs  from  the  marine 
tubular  boiler  only  in  the  arrangement  and  functions  of  the 
tubes.  In  this  boiler  the  tubes  are  vertical,  and  are  water-tubes, 
connecting  the  water  spaces  above  and  below  them.  The  name 
and  combustible  gases  pass  among  and  around  the  tubes  in 
their  passage  to  the  chimney ;  the  heat  being  in  this  case  ap- 
plied to  the  external  surface  of  the  tubes. 

There  is  no  doubt  that,  considered  merely  in  relation  to  the 
transfer  of  heat,  this  arrangement  presents  a  better  form  than 
the  fire-tube.  The  course  of  the  heated  gases  among  the  tubes 
favors  the  absolute  contact  of  the  particles  of  gas  with  the  sur- 
faces of  the  tubes ;  the  tubes  acting  as  "  bafflers."  Moreover,  it 
is  conducive  to  the  rapid  transfer  of  heat  to  a  fluid  for  the  heat 
to  be  applied  to  the  external  surface  of  a  tube  while  the  fluid 
circulates  within,  and  the  vertical  position  of  the  tubes  favors 
this  liquid  circulation.  The  arrangement  permits  also  a  less 
depth  to  the  boiler,  which  is  sometimes,  in  narrow  vessels,  an 
advantage. 

Notwithstanding  these  apparent  advantages,  the  vertical  water- 
tube  boiler,  as  shown,  is  now  seldom  used,  and,  in  fact,  it  had 
but  a  brief  existence  after  its  adoption.  The  chief  defects  are, 
that  when  a  leak  occurs  in  a  tube  there  is  no  possibility  of  stop- 
ping it  except  by  drawing  off  the  water ;  and  even  then  it  is 
difficult  of  access.  If  a  leak  occurs  in  a  tube  of  the  fire-tube 
or  horizontal  tube  boiler,  the  ends  of  the  tube,  which  are  access- 
ible, may  be  closed  by  plugs  and  the  boiler  used  until  repairs 
can  be  conveniently  made.  A  leak  in  a  fire-tube  gives  rise  to  no 
especial  damage,  except  loss  of  water  and  steam ;  but  a  leak 


138  STEAM  GENERATORS. 

from  a  water-tube  may  cause  the  gradual  filling  up  of  the 
interspaces  between  the  tubes  with  salt,  and  thus  impair  the 
draft. 

In  estimating  heating-surfaces,  the  external  surfaces  of  the 
water-tubes  are  calculated.  .  ' 

The  boiler  of  which  Plate  XXII.  is  a  representation  was  con- 
structed for  the  steam  sloop-of-war  Wampanoag,  and  had  the 
following  dimensions  :  Whole  length,  24  feet  4  inches ;  depth, 
9  feet ;  height,  9  feet  5  inches ;  number  of  furnaces,  8  ;  total 
grate-surface,  126  square  feet;  total  heating-surface,  3,028 
square  feet ;  draft  area  across  tubes,  19.04  square  feet ;  smoke- 
pipe,  15  square  feet ;  water- tubes,  2  inches  diameter ;  number 
of  tubes,  2,000. 

Experiments  made  on  the  evaporative  qualities  of  these  boilers 
by  Mr.  B.  F.  Isherwood,  of  the  U.  S.  naval  engineers,  demon- 
strated that  they  were  rather  more  efficient  in  producing  steam . 
than  the  fire-tube  boilers. 

Marine  boilers  of  the  classes  just  described  require  extensive 
bracing,  and  consequently  have  excessive  weight  compared  with 
their  evaporative  powers.  For  this  reason  it  is  not  usual  to  con- 
struct boilers  of  these  forms  for  pressures  of  steam  greater  than 
40  Ibs.,  though  a  recent  instance  is  given  of  such  a  boiler  built 
for  a  steam-yacht  being  built  to  bear  a  pressure  of  100  Ibs.  per 
square  inch.  For  the  higher  pressures  employed  during  the 
present  day  with  the  compound  marine  engines,  the  boilers  are 
usually  made  of  a  cylindrical  form,  on  the  cylinder-tubular  prin- 
ciple. Plates  XXIII.,  Figs.  1,  2,  3  and  4,  represent  a  pair  of 
boilers  made  by  English  manufacturers  for  a  large  steamship 
furnished  with  compound  engines,  the  shells  being  11  feet  in 
diameter,  and  the  iron  of  the  shell  \  of  an  inch  thick.  These 
are  becoming  common  in  marine  constructions,  having  the 
advantage  of  the  greatest  strength  combined  with  the  least 
material. 

222.  The  Locomotive  Boiler. — The  locomotive  boiler  differs 
from  the  cylinder-tubular  boiler  in  having  but  one  system  of 
tubes  direct  from  the  fire-box  or  furnace.  Plate  XXIV.  repre- 
sents the  simplest  form  of  a  locomotive  boiler,  constructed  for 
stationary  purposes.  While  this  cut  represents  all  the  essential 
parts  of  a  locomotive  boiler,  it  has  not  the  exact  form  suitable 
for  the  railroad  engine.  The  number  and  dimensions  of  the  tubes 
in  the  railroad  locomotive  are  greater,  and  in  other  respects  the 


STEAM  GENERATORS. 


138* 


STEAM  GENERATORS. 


138f 


STEAM  GENERATORS. 


138J 


4  *  , 


STEAM  GENERATORS. 


139t 


STEAM  GENERATORS. 


PLATE  XXVI.— Upright  Boiler. 


139$ 


STEAM  GENERATORS. 


PLATE  XXVII.  — Fire-Engine  Boiler. 


STEAM  GENERATORS.      .  139 

railroad-locomotive  boiler  presents  features  peculiar  to  its  adap- 
tation to  a  particular  purpose,  but  the  essential  parts  of  all 
such  boilers  are  exhibited  in  the  plate.  The  fire-box  is  rect- 
angular in  cross-section,  and  the  tubes  pass  directly  from  the 
fire-box  to  the  smoke-connection,  or  smoke-box. 

It  will  be  seen  from  the  construction  that  the  fire-box  is  an 
isolated  chamber,  separated  entirely  from  the  sides  of  the  boiler, 
and  surrounded  by  water.  The  sides  and  top  being  flat,  and 
being  subjected  to  external  pressure,  require  to  be  strongly 
stayed  to  the  shell.  The  crown-plate  is  stayed  to  the  upper 
part  of  the  shell,  and  the  side-plates  and  shell  are  connected 
by  sockets  and  bolts,  the  stays  acting  as  struts  as  well  as  ties. 
The  shell,  dome,  and  tubes  are  constructed  on  the  same  prin- 
ciples as  are  applicable  to  the  cylinder-tubular  boiler.  The 
heating-surface  comprises  the  interior  surface  of  the  fire-box 
and  the  interior  surfaces  of  the  tubes.  Plate  XXV.  represents 
a  set  of  three  locomotive  boilers  erected  and  connected  for 
stationary  purposes. 

The  locomotive  boiler  is  the  type  of  a  large  class  of  boilers, 
the  distinctive  feature  of  which  is  that  the  tubes  pass  directly 
from  the  furnace,  or  fire-box.  For  railroad  engines  various 
modifications  are  used,  each  establishment  usually  having  a 
special  form  of  construction.  In  some,  a  bridge  and  combus- 
tion-chamber are  introduced,  especially  if  the  fuel  is  to  be 
bituminous  coal  or  wood.  For  a  special  description  of  the 
forms  in  general  use  in  this  country,  the  student  is  referred  to 
the  work  of  Mr.  A.  L.  Holley  on  "American  Railway 
Practice." 

223.  A  modification  of  the  locomotive  boiler,  much  used  for 
portable  and  stationary  engines,  is  known  as  the  Upright  JB oiler, 
an  illustration  of  which  is  given  in  Plate  XXYI.     The  sim- 
plicity of  construction,  convenience  of  access,  and  small  space 
occupied  by  these  boilers,   combined    with  their   evaporative 
qualities  and  strength,  and  combining,  as  they  do,  the  chimney 
with  natural  draft  with  the  upright  shell,  render  them  pecu- 
liarly adaptable  for  some  conditions  of  use. 

224.  A   form   of   this   boiler,  which    demands   special   in- 
terest and  attention,  is  found  in  the  Fire-Engine  Boiler  repre- 
sented in  Plate  XXVII.     This  is  essentially  an  upright  boiler 
of  the  locomotive  type,  but  its  peculiarity  consists  in  the  great 
number  of  tubes,  and  the  great  extent  of  heating-surface,  compar- 
ed with  the  cubic  dimensions  and  the  water -space.     To  facilitate 


14:0  STEAM  GENERATORS. 

the  sudden  and  quick  raising  of  steam,  the  tubes  are  compara- 
tively thin  (usually  made  of  brass  or  copper).  This  permits 
not  only  the  introduction  of  a  larger  number  in  a  given  space, 
but  the  thinness  of  the  tubes  lessens  the  time  for  the  first  de- 
velopment of  steam. 

The  cut  exhibited,  Plate  XXYIL,  is  from  a  drawing  kindly 
furnished  by  the  Amoskeag  Manufacturing  Co.,  of  Manches- 
ter, New  Hampshire.  The  dimensions  of  the  boiler  are  as 
follows :  Total  height,  5  feet  4  inches ;  outside  diame- 
ter, 31f  inches ;  number  of  brass  tubes,  301 ;  diameter  of 
tubes,  1J  inch ;  length  of  tubes,  16  inches ;  distance  from 
centre  to  centre  of  tubes,  l^f  inches ;  heating-surface,  157 
square  feet. 

225.  The  following  table  gives  useful  proportions  for  the  con- 
struction of  cylinder  boilers,  cylinder-flue  boilers,  and  cylinder- 
tubular  boilers,  and  the  quantities  of  water  which  the  boilers 
of  the  dimensions  enumerated  will  evaporate.     These  propor- 
tions are   derived   from   current  practice.      In  preparing  the 
columns  of  evaporative  capacities,  an  allowance  of  25  per  cent, 
has  been  made  for  differences  of  management,  draft,  and  fuel, 
which   may  be  met  with,  so  that    the    evaporative  capacities 
mentioned  fall  below  the  best  practical  results  which  may  be 
obtained. 

The  evaporative  powers  are  based  on  the  supposition  that 
coal  is  employed  for  fuel,  and  the  draft  is  produced  by  a 
chimney  of  ordinary  height,  the  combustion  of  fuel  being 
about  9  to  12  pounds  per  hour  on  each  square  foot  of  grate- 
surface,  and  1  pound  of  coal  causing  an  evaporation  of  7  to  9 
pounds  of  water. 

When  steam  in  greater  quantities  than  can  be  furnished  by 
one  of  the  largest  of  these  boilers  is  required,  two  or  more 
boilers  may  be  used  together. 

226.  Sectional  Boilers. — In  all  types  of  boilers  thus  far  con- 
sidered, the  water  and  steam  space  is  either  a  single  chamber, 
as  in  the  plain  cylinder  boiler,  or  a  chamber  traversed  by  tubes, 
through  which,  in  some  cases,  the  heated  gases  find  their  way 
to  the  chimney,  and  in  others  the  circulating  water  finds  its 
way  from  one  part  of  the  water- space  to  another  ;  the  heated 
gases  passing  around  the  outside  of  the  tubes.     The  volume  of 
the  water  is  large  in  proportion  to  the  heating-surface,  and  the 
circulation  of  the  water  is  not  confined  to  prescribed  channels. 


STEAM  GENERATORS. 


141 


TABLE.  XXVIII. 

Table  showing  the  principal  dimensions  of  boilers  of  the  types  named  in  the 
table,  which  have  been  found  suitable  in  practice,  and  the  water  evaporated 
per  hour  by  the  same  from  the  temperatures  of  feed-water  tf/TiO0  and  160^  F. 


DIMENSIONS 

WATER 

E  v  a  p  orated. 

KIND 

SHELL  OF 
BOILER. 

FLUES  OR 
TUBES. 

STEAM 
DRUM. 

GRATE 

HEATING 

per  Hour  at 
80  pounds 
Pressure 

OF 

SURFACE. 

SURFACE. 

from  Tem- 

perature of 

BOILER. 

DlAM. 

LN'TH 

No. 

DlAM. 

DlAM. 

Hl'HT 

' 

60° 

160° 

Inch. 

Feet. 

Inch. 

Inch. 

Inch. 

Sqr.  ft. 

Sqr.  ft. 

Lbs. 

Lbs. 

18 

18.0 

12 

24 

3.8 

42 

202 

221 

PLAIN 

21 

21.0 

14 

28 

5.3 

58 

280 

306 

24 

24.0 

15 

30 

6.8 

75 

363 

395 

CYLINDER 

27 

27.0 

16 

32 

8.6 

95 

458 

501 

30 

30.0 

18 

36 

10.7 

118 

569 

622 

BOILERS. 

33 

33.0 

20 

36 

13.0 

143 

689 

754 

36 

36.0 

20 

40 

15.4 

170 

819 

896 

24 

8.5 

2 

6.5 

12 

24 

3.3 

56 

200 

219 

30 

13.0 

2 

9.0 

15 

30 

6.6 

112 

400 

438 

36 

16.0 

2 

11.0 

18 

30 

9.9 

168 

600 

657 

38 

18.0 

2 

12.5 

22 

36 

12.2 

207 

739 

809 

CYLINDER 

40 

20.5 

2 

13  5 

24 

42 

14.8 

252 

900 

985 

42 

22.0 

2 

14.5 

26 

42 

16.9 

288 

1028 

1126 

FLUE 

44 

23.0 

2 

15.0 

26 

42 

18.4 

313 

1117 

1224 

48 

24.5 

2 

16.0 

27 

48 

21.1 

359 

1282 

1404 

BOILERS. 

52 

26.5 

2 

17.5 

28 

48 

24.9 

423 

1500 

1654 

56 

29.0 

2 

19.0 

30 

54 

29.5 

501 

1789 

1959 

60 

31.5 

2 

20.5 

32 

54 

34.5 

586 

2291 

2092 

66 

36.0 

2 

23.0 

36 

60 

43.8 

745 

2660 

2913 

22 

6.5 

18 

2.0 

12 

24 

2.9 

80 

187 

205 

30 

7.0 

22 

2.5 

15 

30 

5.6 

157 

367 

402 

CYLINDER 

36 

40 

8.5 
9.0 

34 
42 

2.5 
2.5 

18 
22 

30 
36 

8.2 
10.5 

229 
294 

536 

688 

586 
753 

TUBULAR 

44 

47 

11.0 
12.5 

40 
34 

3.0 
3.5 

24 
26 

42 

42 

14.7 
16.6 

409 
466 

957 
1090 

1047 
1193 

BOILERS. 

51 
55 

14.0 
14.5 

34 
42 

4.0 
4.0 

28 
30 

48 
54 

21.1 

592 
742 

1385 
1736 

1516 
1900 

60 

15.0 

52 

4.0 

34 

54 

33^2 

931 

2178 

2383 

66 

15.0 

60 

4.0 

36 

60 

38.3 

1072 

2508 

2744 

1 

.3.0 

85 

199 

218 

LOCOMO- 

5.9 

8.8 

165 
245 

386 
573 

422 
627 

TIVE 

11.4 
14.3 

320 
400 

749 
936 

819 

1024 

BOILERS. 

17.1 
22.5 

480 
630 

1123 

1474 

1229 
1613 

27.7 

775 

1814 

1984 

Moreover,  an  external  shell  is  necessary,  which  must  contain  the 
water  and  steam,  and  generally,  also,  the  system  of  tubes :  this 


142  STEAM  GENERATORS. 

shell  being  subjected  to  the  whole  effect  of  the  steam 
pressure. 

A  system  of  construction  which  has  come  largely  into  use  of 
late  years,  and  which  is  becoming  more  and  more  advanced 
towards  perfection  in  its  mechanical  details,  is  known  in  this 
country  by  the  name  Sectional  Boilers,  and  in  France,  boilers 
with  rapid  circulation,  or  water- circulating  boilers.  This 
system  may  be  said  to  have  originated  with  Mr.  Jacob  Perkins, 
who,  in  1833 ,  obtained  a  patent  in  England  for  improvements 
in  generating  steam,  in  which  he  insisted  on  the  advantages  to 
be  gained  by  causing  the  water  to  circulate  rapidly  over  the 
heating-surfaces  exposed  to  the  direct  action  of  the  fire.  In 
1839  Perkins  obtained  a  patent  for  a  more  complete  apparatus 
involving  this  idea,  under  the  title,  "Apparatus  for  Transmitting 
Heat  by  Circulating  Water."  Steam  generators  constructed 
with  special  reference  to  this  idea  were  extensively  tried,  but 
were  finally  abandoned  for  the  reason  that,  owing  to  practical 
difficulties  in  their  construction,  the  high  pressures  employed, 
and  the  difficulty  of  keeping  them  in  repair,  they  soon  became 
unfit  for  use,  and  it  is  only  from  a  comparatively  recent 
date  that  they  have  again  come  into  use  under  more  favorable 
auspices. 

The  Sectional  Boiler  consists  essentially  of  a  system  of  tubes 
so  arranged  that  a  continuous  circulation  of  the  water  is  main- 
tained through  the  tubes  from  the  mechanical  action  arising 
from  some  portions  of  the  tubes  being  maintained  at  a  higher 
temperature  than  others,  the  heated  and  lighter  water  ascending 
and  the  cooler  and  heavier  water  descending.  The  shell  is  dis- 
pensed with  and  the  heat  applied  directly  by  both  radiation  and 
contact  to  the  exterior  surfaces  of  the  tubes.  The  steam-space 
is  usually  a  large  tube  or  a  system  of  tubes  with  which  the 
various  sections  of  tubes  are  connected,  and  the  various  devices 
which  are  found  in  practical  use  for  connecting  and  arranging 
the- tubes,  so  that  they  shall  form  a  compact  arrangement  with 
all  the  necessary  conditions  for  applying  heat,  for  accessibility, 
and  for  promoting  circulation,  constitute  the  sectional  boilers  of 
the  present  day,  which  usually  take  their  names  from  the  invent- 
ors or  manufacturers. 

The  most  successful  constructions  in  this  country  are  those 
known  as  the  ROOT  BOILER,  the  ALLEN  BOILER,  and  the  PHLEGER 
BOILER.  Plates  XXVIII.  and  XXIX.  represent  the  Root 


THE  CONSTRUCTION  OF  STEAM  GENERATORS.         142* 


PLATE  XXVIII.— The  Root  Boiler. 


THE  CONSTRUCTION  OF  STEAM  GENERATORS. 


r.o 


148*  THE  CONSTRUCTION  OF  STEAM  GENERATORS. 


143f        THE  CONSTRUCTION  OF  STEAM  GENERATORS. 


144:  STEAM  GENERATORS. 

drum  is  connected  with  another,  D,  2J  feet  in  diameter  and  8 
feet  long.  (This  drum  has  been  omitted  in  the  engraving.) 
From  this  latter  drum  the  steam  leaves  the  boiler  by  the  pipe  E. 
These  drums  are  so  arranged  as  to  superheat  the  steam,  being 
surrounded  by  the  products  of  combustion ;  and  in  the  bottom 
of  each  of  the  drums  are  pipes,  F,  G,  connecting  with  II,  the 
lowest  point  of  the  boiler,  to  allow  the  water  carried  over  by  the 
steam  to  drain  back.  The  feed  and  the  water  gauge  and  gauge- 
cocks  are  connected  to  the  steam  and  water  spaces  by  the  pipes 
J,  K,  L,  leading  to  the  steam-drum,  C,  and  the  cross-connection, 
H,  respectively.  .  The  wrought-irori  pipes  are  connected  to  the 
cast-iron  cylinders  at  an  angle  of  20°  from  the  vertical,  the  in- 
ventor claiming  that  as  the  most  effective  position.  The  invent- 
or also  claims  great  facility  for  making  repairs  by  merely  un- 
screwing a  defective  tube  and  substituting  a  good  one. 

DESCRIPTION  OF  THE  PHLEGER  BOILER. 

229.  This  consists  of  a  number  of  wrought-iron  tubes,  connect- 
ed to  cast-iron  tube-plates,  and  set  in  brick- work.     There  are  17 
bent  tubes,  A,  each  2  inches  in  diameter  and  15  feet  long,  so  ar-' 
ranged  as  to  form  the  furnace  and  a  "water-grate,"  being  secured 
at  the  ends  to  cast-iron  tube-sheets,  S,  S1.      There  are,  also,  68 
straight  tubes,  of  the  same  dimensions,  secured  at  the  ends  to 
tube  sheets,  S,  S2.     These  tubes  are  all  connected  with  each 
other  and  the  steam- drum,  D,  by  a  series  of  cast-iron  caps  or 
water-ways,  C1,  C2,  C3,  and  by  the  pipes,  S  P,  S  P1,  these  latter 
being  flanged,  and  secured  to  the  tube-sheets  by  bolts.     The 
steam-drum  is  of  wrought  iron,  and  has  a  diameter  of  2J  and- a 
length  of  12  feet,  and  contains  shelves,  L,  L,  for  the  purpose  of 
preventing  foaming. 

In  France  the  boilers  of  M.  Belleville,  constructed  on  similar 
principles,  enjoy,  perhaps,  the  highest  reputation,  though  many 
others  of  the  same  character  have  been  successfully  introduced. 

230.  Plate  XXXIV.  represents  a  sectional  boiler  of  a  con- 
struction quite  different  from  all  others  which  come  under  this 
denomination.     It  is  called  the  Harrison  Boiler •,  and  is  the  in- 
vention of  Mr.  Joseph  Harrison,  of  Philadelphia.     The  sections 
are  composed  of  hollow  cast-iron  spheres  or  globes  connected 
together  and  communicating  freely  with  each  other.      This 
form   combines,  according  to  the  design  of  the  inventor,  the 
greatest  strength  with  the  least  weight  of  costly  material. 

Sectional  boilers  have  evaporative  powers  not  inferior  to 


STEAM  GENERATORS.  143 

Boiler ;   Plate  XXX.  represents  the  Allen  Boiler,  and  Plate 
XXXI.  the  Phleger. 

The  following  description  of  these  boilers  is  taken  from  the 
report  of  a  committee  appointed  by  the  American  Institute  to 
test  these  boilers,  at  the  exhibition  of  the  Institute  in  1871. 
The  committee  consisted  of  Professor  Thurston,  of  the  Stevens 
Institute  of  Technology,  Messrs.  Robert  Weir  and  Thos.  J. 
Sloan,  whose  experimental  tests  will  be  referred  to  in  another 
place. 

DESCRIPTION  or  THE  ROOT  BOILER. 

227.  This  boiler  consists  essentially  of  80  wrought-iron  tubes, 
each  4  inches  in  diameter,  and  9  feet  long.  These  tubes  are  set  in 
brick-work,  at  an  angle  of  about  30°  from  the  horizontal.     The 
tubes  are  connected  together  by  the  system  of  triangular  plates 
and  crowfeet  represented  in  figures  1  and  2 ;  the  joints  being 
formed  by  the  aid  of  rubber  grummets.    The  boiler  has  a  steam- 
drum,  18  inches  in  diameter,  and  6f  feet  long.     The  superheat- 
ing of  the  steam  is  effected  in  the  upper  portion  of  the  boiler, 
where  the  tubes  are,  like  those  forming  the  water-space,  sur- 
rounded by  the  heated  gases.     The  wrater  was  maintained,  during 
the  trial,  just  above  the  fourth  row  of  tubes. 

The  inventor  claims  that  by  the  contraction  of  the  passages, 
caused  by  the  method  of  connecting  the  tubes,  the  steam  is  dis- 
engaged from  the  water  in  a  comparatively  dry  state. 

The  areas  of  heating  and  grate  surfaces  of  this,  and  of  all  the 
boilers  under  consideration,  are  given  in  the  table  of  results.* 

DESCRIPTION  OF  THE  ALLEN  BOILER. 

228.  This  boiler  possesses  several  novel  features.    There  are  9 
cast-iron  cylinders,  A,  A,  A,  etc.,  each  7  inches  internal  diameter, 
and  11  feet  long ;  and  into  each  of  these  cylinders  18  wrought- 
iron  tubes,  B,  B,  each  3J  inches  in  diameter,  and  closed  at  one 
end  with  plugs,  are  screwed.     In  each  section  of  wrought-iron 
tubes,  9  of  the  tubes  have  a  length  of  3  feet  and  2  inches,  and 
the  remaining  9  have  a  length  of  4  feet  and  5  inches  each. 
The  sections  are  all  connected  by  the  cast-iron  cylinders  to  a 
steam- drum,  C,  2  feet  in  diameter  and  8  feet  long ;  and  this 

*  The  total  of  all  surfaces  exposed  to  contact  with  the  products  of  combus- 
tion is  taken  as  heating-surface. 


STEAM  GENERATORS. 


145 


those  of  the  other  types,  and  possess  the  especial  advantages 
of  occupying  less  space  and  of  being  safe  from  explosions. 
The*  want  of  durability  which  characterized  the  earlier  construc- 
tions has  been  remedied,  to  a  great  extent,  by  improved  modes 


PLATE  XXXIV.— Harrison  Boiler. 

of  construction,  at  least  for  stationary  purposes.  One  disad- 
vantage connected  with  them  consists  in  a  liability  to  rapid 
fluctuations  of  pressure  if  steam  is  drawn  from  them  in  largely 
varying  quantities  in  short  intervals  of  time,  the  volume  of 
water  contained  in  the  boilers  being  small  compared  with  that 
of  other  types.  For  marine  purposes,  when  salt-water  is  used, 
deposits  are  apt  to  be  formed,  which  are  removed  with  diffi- 
culty, and  they  have  not  yet  been  applied  to  any  extent  in 
marine  constructions. 

231.  It  will  be  seen  from  the  above  descriptions,  that  while 
the  same  general  principles  of  combustion  and  of  the  transfer  of 
heat  control  the  detailed  construction  of  steam  generators, 
adaptation  to  special  uses  is  the  consideration  which  gives  rise 
to  many  varieties  of  external  forms. 

The  character  of  the  combustible  has  an  influence  on  the  pro- 
portions of  parts,  and  often  requires  special  consideration.  This 
is  peculiarly  the  case  where  the  combustible  is  entirely  gaseous. 
When  the  gases  to  be  burned  are  drawn  from  blast-furnaces,  and 
are  led  by  conduits  to  the  ignited  coals  of  a  grate,  the  ordinary 
disposition  of  the  parts  of  the  boiler  may  be  followed.  When 
the  gas  is  burned  alone,  the  grate  may  be  suppressed. 

The  gas  from  blast-furnaces  may  be  utilized  not  only  by  em- 
ploying the  heat  of  the  gas,  but  also  in  burning  the  oxide  of 
10 


146  STEAM  GENERATORS. 

carbon,  of  which  it  is  in  part  composed.  In  burning  this  gas 
it  is  not  necessary  to  furnish  air  in  so  great  a  quantity,  and  the 
construction  of  the  furnaces  is  thus  further  simplified.  One 
boiler  is  often  placed  in  such  a  manner  as  to  consume  the  gas 
from  several  furnaces. 

In  the  metallurgical  establishments  of  Creusot  and  Oullins,in 
France,  the  boilers  for  utilizing  the  furnace-gases  are  vertical 
cylinder  boilers  placed  in  a  chimney  lined  with  fire-brick. 

Boilers  somewhat  similar  to  the  locomotive  boiler  are  also  used 
in  France  for  the  same  purpose.  In  England,  vertical  cylinder 
boilers  of  large  diameter  with  interior  flues  are  used  ;  each  boiler 
receiving  the  heated  gases  from  several  puddling  furnaces. 

In  all  cases  where  the  gas  is  not  burned,  the  problem  consists 
in  devising  the  best  mode  of  conducting  it  in  contact  with  the 
greatest  amount  of  heating-surface ;  and  where  a  partial  com- 
bustion also  takes  place  in  the  boiler,  the  necessary  means  of 
continuity  of  combustion  by  a  bed  of  ignited  coals  must  be  pro- 
vided ;  and  with  these  conditions  must  be  combined  the  funda- 
mental requirements  of  durability  and  safety. 

NOTE. — Boilers  with  forced  circulation.  In  all  steam  generators  thus  far  de- 
scribed, and  in  all  others  as  at  present  used,  the  circulation  of  the  water  within 
the  boiler  is  produced  by  a  difference  of  specific  gravity  of  the  heated  water  at 
different  points,  aided  perhaps  by  the  rising  of  bubbles  of  steam.  The  circula- 
tion is  dependent  on  the  evaporation,  as  soon  as  a  constant  working  pressure  is 
reached,  and  is  necessarily  slow.  I  have  made  experiments,  assisted  by 
Messrs.  T.  W.  Mather  and  J.  K.  Klein,  graduate  students  of  the  Sheffield 
Scientific  School,  to  determine  the  efficiency  of  a  forced  circulation  of  the 
heated  liquid.  The  difficulty  of  constructing  very  small  steam  generators 
having  sufficient  strength  to  resist  great  pressure,  and  at  the  same  time  a  high 
rate  of  evaporation  with  reasonable  economy,  has  long  been  recognized.  On 
account  of  this  difficulty  the  use  of  very  small  engines  is  limited.  The  boiler 
in  such  engines  must  have  such  large  proportions  relatively  to  the  engine  that 
it  ceases  to  be  an  economical  apparatus. 

The  object  of  my  experiments  was  to  reduce  the  heating-surface,  and  at  the 
same  time  make  it  more  efficient  by  a  forced  and  continuous  circulation  of  the 
water  in  the  boiler,  through  the  means  of  a  circulating  pump.  Various  com- 
binations and  modes  of  circulation  have  been  tried,  with  results  which  thus  far 
appear  conclusive.  A  steam  generator  of  very  small  volume  and  weight  made 
of  coils  of  gas-pipe  and  consequently  having  a  resistance  of  several  thousand 
pounds  per  square  inch,  has  been  made  to  evaporate  quantities  of  steam  per 
hour  which  by  ordinary  processes  would  require  a  boiler  of  very  much  greater 
volume.  The  principle  of  forced  circulation  has  not  heretofore  been  employed 
for  this  purpose,  but  there  is  reason  to  believe  that  it  may  become  practically 
useful,  especially  for  solving  the  important  problem  of  very  small  steam- 
engines — engines  having  but  a  fraction  of  a  horse-power. 


CHAPTEE  VI. 

THE  CONSTRUCTION  OF  STEAM  GENERATORS. 

232.  WHATEVER  may  be  the  type  of  steam  generator  selected 
for  a  special  purpose,  the  following  fundamental  considerations 
are  involved  in  its  design  and  construction : 

I. — Proportion  of  parts. 
II. — Actual  dimensions. 
III. — Kind,  quality,  and  strength  of  the  materials  employed, 

and  the  mechanical  conditions  of  the  structure. 

% 

The  proper  proportions  of  the  parts  determine  the  economy 
or  efficiency  of  the  apparatus. 

On  the  actual  dimensions  depends  the  capacity  for  produc- 
ing steam,  or,  as  it  is  sometimes  expressed,  i\\Q  power  oi.  the  boil- 
er ;  and  on  the  kind,  quality,  and  strength  of  the  materials  em- 
ployed, and  the  mechanical  perfection  of  the  structure,  depend 
not  only  the  first  cost,  but  also  the  strength  of  the  structure  and 
its  durability. 

233.  Proportion  of  Parts. — The  parts  of  which  the  relative 
proportions  require  special  consideration,  are  those  which  de- 
termine the  combustion  of  the  fuel  and  the  transfer  of  heat. 

It  is  obvious  that  the  first  object  to  be  attained  is  the  thorough 
and  complete  combustion  of  the  fuel.  If  any  combustible 
gases  or  any  portion  of  the  fuel  in  the  form  of  smoke  escape 
from  the  chimney,  a  direct  loss  occurs,  which  should  be  pre- 
vented if  possible.  This  question  may  be  discussed  without 
reference  to  the  question  of  transfer  of  heat,  in  which  the  pro- 
portion of  heating  surface  is  chiefly  to  be  considered ;  and  the 
elements  on  which  the  discussion  depends  are  those  parts  of 
the  apparatus  which  control  the  introduction  of  air  to  the  fuel, 
and  the  quantity  and  disposal  of  the  fuel  with  which  the  air 
comes  in  contact. 


14:8  THE  CONSTRUCTION  OF  STEAM  GENERATORS. 

234.  Chimneys. — The  chimney,  in  all  cases  in  which  the  draft 
is  produced  by  a  simple  "  chimney-draft,"  performs  the  func- 
tions of  a  machine,  and  its  dimensions  (its  height  and  cross-sec- 
tion), taken  in  connection  with  the  area  of  the  grate,  and  the  sur- 
face of  contact  of  the  fuel  exposed  to  the  action  of  the  air,  are 
the  principal  elements  on  which  not  only  complete  or  perfect 
combustion,  but  the  quantity  of  fuel  burned  in  a  given  time,  de- 
pend. In  boilers  provided  with  any  other  means  of  draft,  such 
as  the  steam  jet,  or  the  blower,  the  dimensions  of  the  chimney 
are  not  so  important.  In  almost  all  stationary,  and  in  nearly  all 
marine,  boilers,  the  draft  is  produced  solely  by  a  chimney,  which 
forms  an  indispensable  and  important  part  of  the  apparatus. 
The  determination  of  the  proper  proportions  between  the  heat- 
ing surface  and  the  grate  surface  depends  on  the  initial  tem- 
perature of  the  gases ;  and  as  the  initial  temperature  varies 
with  the  rate  of  combustion,  or  the  height  of  the  chimney,  the 
height  of  the  chimney  indirectly  enters  into  the  consideration 
of  this  proportion.  , 

It  is  well  known  that  the  draft  of  a  chimney  is  caused  by  a 
difference  of  pressure  at  the  base  of  the  chimney,  acting  in  an 
upward  direction,  due  to  the  difference  between  the  weight 
of  the  heated  gases  in  the  chimney,  and  a  column  of  equal 
height  and  cross-section  of  the  external  air.  This  difference  of 
pressure  is  easily  found.  If  we  take  a  unit  of  area  of  the 
cross-section — one  square  foot  for  instance — the  weight  of  the 
column  of  external  air  wTill  be  the  height  of  the  chimney  mul- 
tiplied by  the  density  of  the  external  air,  and  the  weight  of  the 
column  of  heated  gases,  of  equal  height,  will  be  equal  to  the 
height  of  the  chimney  multiplied  by  the  density  of  the  heated 
gases.  If  H  be  the  height  of  the  chimney,  D  the  density  of 
the  external  air,  and  D'  the  density  of  the  heated  gases,  the 
difference  of  pressure  referred  to  will  therefore  be,  in  algebraic 
symbols, 

p  =  H  D  —  H  D'  =  H  (D  —  DX) 

This  unbalanced  pressure  acts  as  a  motive  force  to  drive  the 
heated  gases  through  the  chimney  and  out  at  the  top.  In  order 
to  find  what  height  of  column  of  the  external  air  would  pro- 
duce this  pressure,  acting  simply  by  its  weight,  we  have  to 
divide  the  pressure  by  the  density  of  the  external  air,  and  will 
have — 


THE  CONSTRUCTION  OF  STEAM  GENERATORS.          149 

p  /  D  —  D'  \ 

-±—  =   H(-          -  ) 

D  V        D         / 

It  is  a  well-known  law  of  dynamics  that  the  theoretical 
velocity  with  which  the  air  would  enter  the  chimney,  if  there 
were  no  resistance,  would  be  found  by  the  equatio 


\\  / 

from  which  the  theoretical  velocity  of  access  o£  external'  41? 

would  be 


D 

V  — 

'    "  "         D 


The  values  of  D  and  D'  may  be  readily  found  from  princi- 
ples already  enunciated.  If  DO  represent  the  density  or  weight 
of  a  cubic  foot  of  air  at  32°  and  at  atmospheric  pressure,  given 
on  page  66,  the  weight  at  any  other  temperature  will  be  D  —  DO  x 

rp 

—  T!  being  the  temperature  of  the  external  air  generally  higher 

than  TO  the  absolute  temperature  of  melting  ice. 

If  the  external  air  be,  for  instance,  at  60°  F.,  TX  will  be  459.4 
4-  32  +  60  =  551.4,  absolute  temperature.  DO,  found  from  the 
table  on  page  66,  is  .08073.  TO  —  459.4  +  32  ==  491.4  :  from 
these  given  quantities, 


-       - 

D  =  0.0873  x      ?    =  0.07182 
551.4 

For  the  weight  of  a  column  of  the  heated  gases  of  the  chim- 
ney, having  a  base  of  one  square  foot,  a  similar  process  is  to  be 
followed.  The  chimney  gases  being  composed  of  nitrogen, 
oxygen,  and  carbonic  acid,  principally,  it  is  necessary  to  ascer- 
tain first  the  proportions  of  each  of  these  gases  in  a  cubic  foot, 
at  atmospheric  pressure  and  at  the  temperature  of  the  heated 
gases.  Results  of  experiments  made  by  Combes,  Johnson, 
and  others,  indicate  that  these  gases  are  found  in  the  pro- 
ducts of  combustion  in  the  following  proportion,  nearly, 
when  the  fuel  is  ordinary  coal.  The  proportions  in  one  cubic 
foot  are  : 


150          THE  CONSTRUCTION  OF  STEAM  GENERATORS. 

Carbonic  acid 0.10 

Nitrogen 0.79 

Oxygen 0.11 

These  proportions  are  adopted  by  Morin  and  Tresca  after 
comparing  the  results  of  various  experiments.  At  32°  F.  and 
atmospheric  pressure,  one  cubic  foot  of  the  heated  gases  would 
therefore  weigh,  according  to  the  table,  page  66 — 

Carbonic  acid 10  x  .12344:  =  0.01234 

Nitrogen 79  x  .07860  =  0.06209 

Oxygen. 11  x  .08926  =  0.00981 

Weight  of  one  cubic  foot =  0.08424  Ibs. 

If  we  suppose  the  temperature  of  the  heated  gases  to  be 
500°  F.,  the  density  D'  at  500°  will  be 

m  4.Q1     A0 

0.08424  -°  =  0.08424  x 


T,  459.4°  +  32°  +  500° 

The  velocity  v  determined  from  this  formula  is  not,  however, 
that  with  which  the  external  air  will  enter  the  chimney.  Ke- 
sistance  is  offered  to  the  passage  of  air  through  the  grate,  through 
the  bed  of  fuel,  and  through  the  flues  and  chimney.  These 
resistances  do  not  admit  of  theoretical  determination,  and  can 
only  be  found  by  direct  experiment.  They  are  proportional  to 
the  square  of  the  actual  velocity,  and  depend  on  the  diameter 
and  length  of  the  flues  and  chimney,  the  thickness  of  the  bed 
of  fuel,  and  the  state  of  division  of  the  fuel. 

The  experiment  of  Pecl&t  led  him  to  propose  the  formula 
for  the  actual  velocity  essentially  as  given  below : 


d 


In  the  formula  of  Peclet  he  supposes  the  air  to  enter  the 
chimney  at  32°  F.,  and  the  density  of  the  heated  gases  to  be 


THE  CONSTRUCTION  OF  STEAM  GENERATORS.          151 

the  same  as  that  of  air  at  the  same  temperature,  so  that  his  for- 
mula is : 


=        2  g  H 


(a)  in  this  formula  being  3-^-,  and  t  the  temperature  Cent,  of 
the  heated  gases. 

For  heights  of  10,  20,  and  30  metres,  he  finds  for  the  ordi- 
nary condition  of  chimneys  of  manufacturing  establishments  : 
E  =  29.98,  33.49,  and  38.29,  and  v'  =  .18  v.  v'  =  .17  v.  v' 
=  .16  v. 

In  Peclet'  s  formula  K  represents  a  coefficient  of  friction,  L 
and  d  the  length  and  diameter  of  the  chimney  and  flues,  and 
A  a  coefficient  of  resistance  of  the  grate. 

The  values  of  the  velocity  of  access  of  air  found  by  Peclet 
for  heights  of  10,  20,  and  30  metres,  or  32.8  feet,  65.6  feet,  and 
98.4  feet,  were  5.1  feet,  8  feet,  and  9.18  feet  per  second,  or 
18,360,  28,800,  and  32,948  feet  per  hour.  These  velocities,  di- 
vided by  the  number  of  cubic  feet  of  air  required  to  burn  one 
pound  of  fuel,  will  give  the  quantity  of  fuel  burned  per  hour 
for  each  square  foot  of  section  of  the  chimney,  the  section  of 
the  chimney  bqing  supposed  equal  to  the  free  surface  of  the 
grate.  The  volume  of  air  required  to  burn  one  pound  of  fuel 
of  a  given  kind  is  given  in  the  table  page  93.  In.  the  ordinary 
process  of  combustion  in  a  grate,  it  is  apparent  that  some  of  the 
air  which  enters  must  escape  contact  with  the  fuel,  and  enter 
the  chimney  as  air.  The  quantity  which  thus  escapes  has  been 
usually  assumed  equal  to  the  quantity  which  is  required  for 
combustion,  or,  in  other  words,  the  quantity  which  enters  the 
furnace  has  been  estimated  to  be  double  the  quantity  required 
for  combustion. 

This  was  the  deduction  usually  made  from  the  experiments 
made  by  Prof.  W.  E.  Johnson,  Peclet,  and  by  a  commission 
appointed  by  the  English  Board  of  Admiralty.  But  more  re- 
cent experiments,  especially  those  made  by  the  Industrial 
Society  of  Mulhouse,  indicate  that  this  is  too  large  an  allow- 
ance, and  it  is  stated  by  Morin  and  Tresca  as  the  result  of  the 
examination  of  all  the  experiences  on  the  subject,  that  about 
one  and  seventy-five  huiidredths  of  the  amount  actually  re- 
quired for  combustion  appears  to  be  nearer  the  true  amount  to 


152          THE  CONSTRUCTION  OF  STEAM  GENERATORS. 

be  allowed.  This  corresponds  to  the  composition  of  the  heated 
gases  which  has  been  already  given.  According  to  this  result, 
the  quantity  of  air  actually  drawn  into  the  furnace  for  each 
pound  of  fuel  burned  will  be  about  250  feet.  The  consumption 
of  fuel  per  square  foot  of  section  of  the  chimney  will  then  be, 
for  the  heights  above  given,  viz. : 

Heights,  32.8  65.6  98.4 

Pounds,  73.4          115.1          137.8 

If  it  be  assumed  that  each  square  foot  of  section  of  the  chim- 
ney corresponds  to  8  square  feet  of  grate  surface,  the  above 
figures  will  give  for  the  rate  of  combustion  on  each  square  foot 
of  grate  surface, 

Pounds,  9.2  14.8  17.2 

These  results  seem  to  be  the  nearest  that  can  be  attained  by 
combining  theoretical  considerations  with  experimental  deduc- 
tions. The  conditions  which  exist  in  different  chimneys  and 
furnaces  in  regard  to  the  resistances  are  so  complex  and  various 
that  no  theoretical  formula  will  give  results  which  can  be  con- 
sidered even  approximately  correct.  A  comparison  of  the  re- 
sults obtained  by  the  partly  empirical  formula  of  Peclet,  applied 
to  ordinary  conditions  of  practice,  with  numerous  examples,  in 
which  the  quantity  of  fuel  burned  and  the  dimensions  of  the 
chimneys  are  given,  has  led  to  the  suggestion  of  the  following 
practical  table  of  heights,  and  quantities  of  fuel  burned  per 
square  foot  of  section  of  the  chimney  per  hour.  This  table  is 
intended  only  to  give  approximate  quantities,  and  although  in- 
stances are  given  which  differ  from  the  table  considerably,  it  is 
to  be  borne  in  mind  that  in  constructing  a  chimney  an  excess 
of  height  should  be  chosen,  since  the  draft  may  be  afterwards 
regulated  by  a  damper,  and  no  serious  error  in  choice  is  likely 
to  occur. 

The  diameters  at  the  top  suitable  for  the  given  heights  may 
be  estimated  from  1  foot  for  the  least  height,  to  4  feet  for  the 
greatest. 

This  table  was  constructed  by  collecting  reliable  data  from 
experiments,  and  plotting  the  heights  corresponding  to  the  rate 
of  combustion  found.  A  curve  drawn  through  the  mean  posi- 


THE  CONSTRUCTION  OF  STEAM  GENERATORS. 


153 


tions  furnished  the  means  of  interpolating  the  figures  in  the 
table. 


TABLE  XXIX. 

Showing  heights  of  chimneys  for  producing  certain  rates  of  combustion  per  square 
foot  of  area  of  section  of  the  chimney ; 


Heights  in  Feet. 


20 60 

25 68 

30 76 

35 84: 

40 93 

45 99 

50 105 

55 Ill 

60 116 

65 121 

70 ,..  126 

75 131 

80 135 

85 139 

90 144 

95.. 148 

100 152 

105 156 

110..  160 


Pounds  of  coal  burned 
per  hour  per  square 
foot  of  section  oi 
chimney. 


Pounds  of  coal  burned 
per  hour  per  square 
foot  of  grate,  the 
ratio  of  grate  to«eo- 
tion  of  chimney 
being  8  to  1. 


7.5 

8.5 

9.5 

10.5 

11.6 


12.4 
13.1 
13.8 
14.5 
15.1 
15.8 
16.4 
16.9 
17.4 
18.0 
18.5 
19.0 
19.5 
20.0 


It  appears  from  the  table  that  a  difference  of  height  of  8  feet 
corresponds  to  a  difference  in  rate  of  combustion  of  about  one 
pound  per  square  foot  of  grate  surface,  the  ratio  of  the  grate 
to  the  chimney  section  being  8  to  1. 

This  result  was  verified  in  particular  cases  as  approximately 
true. 

The  quantities  given  in  the  table  refer  to  the  average  con- 
ditions of  chimneys  of  steam  generators. 

235.  Grate  Surface. — The  height  of  the  chimney,  taken  in 
connection  with  the  temperature  of:  the  heated  gases,  determines, 


154          THE  CONSTRUCTION  OF  STEAM  GENERATORS. 

as  has  been  shown,  the  rate  of  combustion.  This  is  true  only 
when  the  fuel  is  so  disposed  as  to  insure  complete  or  perfect 
combustion.  If  air,  after  having  come  in  contact  with  incan- 
descent fuel,  and  after  the  oxygen  combines  with  carbon  to 
form  carbonic  acid,  comes  again  in  contact  with  fuel  at  a  lower 
temperature,  the  carbonic  acid  usually  parts  with  a  portion  of 
its  oxygen,  and  carbonic  oxide,  which  is  a  highly  combustible 
gas,  is  formed  and  passes  off  by  the  chimney.  The  combustion 
will  then  be  incomplete.  The  fuel  must  therefore  not  only  be 
in  just  sufficient  quantity,  but  it  must  be  properly  disposed. 

In  practice  it  is  spread  over  a  grate  to  the  depth  of  7  to  10 
inches,  and  the  grate  is  made  to  bear  a  certain  proportion  to 
the  section  of  the  chimney. 

By  free  surface  of  the  grate  is  to  be  understood  the  openings 
between  the  grate  bars,  further  diminished  as  they  are  in  area 
by  the  stopping  of  the  passages  by  the  lumps  of  fuel. 

It  is  usual  to  make  the  openings  between  the  bars  j  to  f  of 
the  whole  area  of  the  grate  surface.  If  these  openings  are  in- 
sufficient, there  will  be  a  deficiency  of  air  and  incomplete  com- 
bustion will  result. 

The  proportions  of  the  grate,  section  of  chimney  and  flues, 
and  the  heating-surface,  are  generally  given  in  terms  of  the 
grate  surface,  which  is  assumed  as  unity.  The  grate  being  1, 
the  following  proportions  have  been  found  to  answer  in  prac- 
tice for  the  free  spaces  between  the  grate  bars : 

Plain  cylinder  boiler 0.25 

Cornish  boiler 0.23 

French  boiler 0.34 

Tubular  and  flue  boilers 0.40 

These  numbers,  multiplied  by  the  total  area  of  the  grate  sur- 
face, will  give  the  total  area  of  openings  between  the  bars.  For 
burning  bituminous  coal  or  wood  it  is  usual  to  add  openings  to 
the  amount  of  about  ^th  of  the  area  of  the  grate  by  holes 
through  the  furnace  doors. 

Such  additional  apertures  are  sometimes  placed  behind  the 
bridge,  and  air  is  often  forced  into  the  furnace  by  a  steam  jet, 
to  complete  the  combustion  and  prevent  smoke. 

There  does  not  seem  to  be  any  uniformity  of  practice  in  re- 
gard to  the  proportion  between  the  total  grate  surface  and  the 


THE  CONSTRUCTION  OF  STEAM  GENERATORS.          155 

cross-section  of  the  chimney,  or  the  draft  area  over  the  bridge 
walls. 

According  to  the  experiments  of  Mr.  Isherwood,  the  best  pro- 
portion for  the  draft  area  is  -J-  of  the  area  of  the  grate.  Many 
constructors,  however,  make  it  greater,  amounting  in  some  cases 
to  1  and  -J-.  Others  make  it  less,  TV  being  not  uncommon.  The 
proportion  will  be  assumed  as  best  at  •§-,  the  thickness  of  the  bed 
of  fuel  being,  under  these  conditions,  about  7  inches.  The 
cross-section  of  the  chimney  may  have  the  same  proportion, 
though  the  section  of  the  chimney  at  the  top  is  generally  less 
than  at  the  base.  The  cross-areas  of  the  different  sets  of  flues 
generally  diminish,  also,  in  going  towards  the  chimney. 

236.  Heating  Surfaces. — The  heating-surfaces  of  a  boiler  have 
already  been  denned  to  be  all  those  surfaces,  or  plates ,  of  the 
boiler  which  serve  to  transmit  heat  from  the  furnace  or  heated 
gases  to  the  water  or  steam  within  the  boiler.  From  the  laws 
of  transfer  of  heat  it  appears  that  the  quantity  of  heat  trans- 
mitted by  any  surface  depends  on  the  extent  of  the  surface,  and 
the  difference  of  temperature  between  the  source  of  heat  and 
the  absorbent ;  or,  in  the  case  of  steam  generators,  the  difference 
in  temperature  of  the  incandescent  fuel,  or  heated  gases,  and 
the  water  in  the  boiler. 

The  arrangement,  or  disposition,  of  the  heating-surfaces  has 
been  already  given  in  the  descriptions  of  the  various  types  of 
boilers.  The  extent  or  amount  of  heating-surface  is  fixed  with 
reference  to  the  initial  temperatures  of  the  furnace  and  gases; 
or,  since  these  temperatures  are  proportional  to  the  rate  of  com- 
bustion, the  extent  of  heating-surface  will  depend  on  the  rate 
of  combustion  to  be  employed.  The  extent  of  heating-surface 
must  evidently  also  be  in  proportion  to  the  absolute  quantity  of 
fuel  burned  in  a  given  time,  or,  what  is  the  same  thing,  it  must 
have  a  direct  relation  to  the  grate-surface. 

To  illustrate  this  clearly,  in  the  following  diagram,  Fig.  7, 
let  o  F  represent  a  flue  or  tube  having  an  extent  of  heating 
surface  from  the  initial  point  o  to  the  right,  o  r,  equal  to  the 
heating  surface  of  a  given  boiler,  not  taking  into  account  the 
surface  exposed  to  direct  radiation ;  the  point  o  being  the  en- 
trance to  the  flue.  With  a  given  rate  of  combustion  let  o  A 
represent  the  initial  difference  between  the  temperature  of  the 
heated  gases  and  the  water  in  the  boiler,  the  temperature  of  the 
latter  being  constant.  The  curve  A  b,  drawn  according  to  the 


156 


THE  CONSTRUCTION  OF  STEAM  GENERATORS. 


law  of  diminution  of  temperature,  will  represent  the  curve  of 
temperatures ;  at  the  point  b  we  may  suppose  the  temperature 
to  have  been  reduced  to  about  600°  F.  Suppose  now  a  different 
and  higher  rate  of  combustion  to  be  maintained,  the  initial  dif- 
ference in  temperature  may  be  represented  by  o  A"  and  the 
curve  A"  b"  will  represent  the  curve  of  temperature  corre- 
sponding to  this  higher  temperature.  It  is  evident  from  the 
diagram,  that  to  reduce  the  temperature,  of  the  heated  gases  to 
the  same  final  temperature,  600°,  the  heating  surface  will  have 
to  be  extended  to  F'.  And  for  another  and  higher  rate  of  com- 
bustion, the  initial  difference  of  temperature  being  o  A//X,  the 
heating  surface  will  have  to  be  extended  to  F'".* 


Fig.  7. 


*  This  increase  in  practice  is  not  generally  made  by  extending  the  heating- 
surface  in  the  direction  of  the  chimney,  but  by  enlarging  the  cross-section. 


THE  CONSTRUCTION  OF  STEAM  GENERATORS.        157 

The  curves  showing  the  variations  in  the  quantities  of  heat 
transferred  may  be  found  from  the  curves  of  temperature  by 
taking  the  value  of  any  ordinate  of  the  curve  of  temperature 
and  raising  it  to  the  power  whose  index  is  1.233  according  to 
Dulong  and  Petit,  or  to  the  second  power,  according  to  Ran- 
kine,  and  the  total  quantities  of  heat  transferred  through  the 
heating-surface  will  be  represented  by  the  areas  included  be- 
tween the  axis  o  F,  the  curves  of  quantities  of  heat,  and  the 
extreme  limiting  ordinates  of  the  heating-surface. 

The  figure  shows  that  if  the  heating-surface  remains  con- 
stant there  will  be  an  additional  loss  of  heat  for  each  additional 
increase  of  temperature.  The  only  mode  of  preventing  such 
loss  is  by  extending  the  heating-surface.  The  proper  rate  of 
increase  of  heating-surface  may  be  derived  approximately  from 
experiments. 

The  following  results  are  taken  from  the  published  records 
of  experiments  made  for  the  IL'S.  Navy  under  the  direction  of 
Mr.  B.  F.  Isherwood.  The  first  horizontal  line  represents  the 
quantities  of  anthracite  coal,  in  pounds,  burned  on  each  square 
foot  of  grate-surface  in  a  marine  tubular  boiler,  the  heating- 
surface  remaining  constant  and  having  a  ratio  of  25  to  1  to  the 
grate-surface. 

The  second  horizontal  line  represents  the  pounds  of  water 
evaporated  under  atmospheric  pressure  from  212°  F.  by  one 
pound  of  coal. 

Pounds  of  coal  burned  per  hour. 

6,       8,      10,    12,   14,  16,  18,  20,  22,  24 
10.5,  10.4,  10.1,  9.5,  8.9,  8.2,  7.7,  7.3,  7.0,  6.8. 

Pounds  of  water  evaporated. 

A  second  series  of  experiments  is  furnished  by  Mr.  D.  K. 
Clark  in  his  excellent  work  on  Railway  Machinery,  in  which 
he  gives  the  amounts  of  evaporation  for  different  boilers  with 
varying  rates  of  combustion,  and  varying  proportions  of  heat- 
ing-surface. The  following  results  are  extracted  from  his  work. 
The  first  horizontal  line  of  figures  gives  the  quantities  of 
coke  burned  per  hour  on  each  square  foot  of  grate-surface. 
The  second  gives  the  quantities  of  heating-surface  in  square 
feet  required  to  preserve  the  evaporation  constant  for  each 
pound  of  coke,  and  equal  to  9  pounds  of  water  for  each  pound 
of  coke  burned. 


158          THE  CONSTRUCTION  OF  STEAM  GENERATORS. 
Pounds  of  coke  burned  on  each  square  foot  of  grate. 

14,  19,  25,  31,  38,  47,  56,  65,  76,  87,  98,  110,  125,  139, 153. 
30,35,40,45,50,55,60,65,70,75,80,  85,    90,    95,  100. 

Heating-surface  for  each  square  foot  of  grate. 

These  two  sets  of  experimental  results  serve  to  show  how,  in 
the  first  place,  the  economic  evaporation  varies  with  the  rate  of 
combustion,  the  heating-surface  remaining  the  same ;  and  in 
the  second,  how  the  heating-surface  must  vary  if  the  rate  of 
evaporation  remains  constant. 

Inasmuch,  however,  as  it  is  impossible  to  vary  the  heating- 
surface  at  will,  after  a  steam  generator  is  constructed,  it  is  cus- 
tomary to  fix  the  extent  of  this  surface  according  to  average 
conditions  of  use,  taking  into  account  average  rates  of  com- 
bustion. 

The  following  proportions  represent  as  near  as  can  be  ascer- 
tained the  usual  rules  of  practice.  The  grate-surface  being 
1,  the  heating-surfaces  are  for 

Plain  cylinder  boilers 10  to  15  average  12 

Cornish  boilers 30  to  40        "  35 

French  cylinder  boilers 25  to  40        "  33 

Cylinder  "flue  boilers 17  to  25        "  21 

Cylinder  tubular  boilers  (chim- 
ney draft). , 25  to  30        "  28 

Traction-engine  boilers. .....  "  32 

Marine  tubular  and  flue  boil- 
ers— French,   English,    and 

American  practice "  25 

Locomotive  boilers 40  to  100        "  75 

The  rates  of  combustion  per  hour  and  per  square  foot  of 
grate,  in  ordinary  practice,  are,  according  to  Rankine, 

Slowest  rate  in  Cornish  boilers . .  4  Ibs.  per  hr. 

Ordinary  rate 10     "       " 

Ordinary  rate  in  factory  boilers .  12  to  16     "       " 

Ordinary  rate  in  marine  boilers.  16  to  24     "       u 

Locomotive  boilers 40  to  120  "      " 

A  general  rule  is  given  by  Morin  and  Tresca  for  the  quan- 
tity of  coal  consumed  per  hour,  viz. :  that  "  boilers  will  have 


THE  CONSTRUCTION  OF  STEAM  GENERATORS.          159 

favorable  conditions  of  heating-surface,  if  the  consumption  of 
fuel  per  square  foot  of  heating-surface  does  not  surpass  the 
quantities  given  below :  " 

"  Land  boilers,  0.6  pound  of  coal  consumed  for  1  square  foot 
of  heating  surface." 

"  for  marine  boilers,  0.5  pound  per  square  foot." 

"  For  locomotive  boilers,  0.8  pound  per  square  foot." 

This  corresponds  to  a  proportion  of  heating-surface  for  land 
boilers  (French  boilers)  of  24  to  1 ;  for  marine  boilers,  28  to  1, 
and  for  locomotive  boilers,  70  to  1 ;  and  to  a  rate  of  combus- 
tion per  square  foot  of  grate  of  14.4  Ibs.,  14.0  Ibs.,  and  56  Ibs. 

It  is  customary  in  England  to  estimate  the  heating-surface 
by  the  amount  required  to  evaporate  one  cubic  foot  of  water 
from  60  at  212°,  and  a  cubic  foot  of  water  evaporated  per  hour 
is  estimated  to  give  a  nominal  horse-power.  Armstrong's  rule, 
"  a  yard  of  heating-surface  to  a  horse-power,"  for  the  old  wagon 
boiler,  is  founded  on  this  idea,  since  it  requires  about  one  square 
yard  of  heating-surface,  and  one  square  foot  of  fire-grate,  to 
evaporate  one  cubic  foot  of  water  in  these  boilers.  The  pro- 
priety of  this  rule  is,  however,  questionable,  since  it  is  not  ap- 
plicable to  other  forms  of  boilers,  and  the  term  horse-power,  as 
applied  to  boilers,  is  improper,  unless  the  pressure  of  the  steam 
is  taken  into  account,  and  even  then  it  is  to  be  estimated  inde- 
pendently of  the  engine  in  which  the  steam  is  utilized,  and  is 
an  arbitrary  measure  of  capacity. 

The  quantity  of  heating-surface  necessary  to  evaporate  one 
cubic  foot  of  water  is  however  a  proper  basis  of  estimate  of 
heating-surface,  provided  the  type  of  boiler  and  the  rate  of 
combustion  are  given,  and  it  is  usual  in  such  cases  to  state  how 
many  pounds  of  water  will  be  evaporated  by  each  pound  of 
coal ;  the  amount  of  heating-surface  is  in  this  manner  connect- 
ed with  the  rate  of  combustion. 

In  a  recent  report  of  a  committee  of  the  Franklin  Institute 
(Journal  of  the  Franklin  Institute,  1872),  the  mode  of  estimat- 
ing heating-surfaces  of  Cornish  boilers  by  Messrs.  Easton 
and  Anderson,  of  London,  is  given,  from  which  it  appears 
that  the  area  of  the  under-side  of  the  shell  and  the  area  of 
the  top-half  of  the  flues  constitute  the  heating-surface ; 
and  of  this  12  square  feet  are  allowed  to  evaporate  one 
cubic  foot  of  water  per  hour  from  60,  and  at  212°  F.  The  com- 
mittee give  also  the  heating-surfaces  of  various  boilers  re- 


160          THE  CONSTRUCTION  OF  STEAM  GENERATORS. 

quired  to  evaporate  one  cubic  foot  of  water  per  hour  at  212° 
viz. : 

Plain  cylinder  boilers  (corresponding  to  the 

old  wagon  boiler) 8.8  square  feet. 

Galloway    multi tubular   boiler    (water -tube 

'    boiler) 8.5  " 

Marine  tubular  boiler 14  " 

Double-flue  Cornish 11.7  " 

For  these  the  rate  of  combustion  is  such  that  the  total  heat- 
ing-surfaces are  sufficient  to  evaporate  nine  pounds  of  water  for 
one  pound  of  coal. 

The  following  conclusions  are  deduced  by  the  committee 
from  Mr.  Isherwood's  experiments.  The  boilers  of  various 
steamships  on  which  experiments  were  made,  with  the  results, 
are  indicated  by  the  names  of  the  vessels : 

Jacob  Bell Marine  tubular 19  12  11 

Mt.  Vernon «  19  10.5  10.5 

Valley  City "  16  11.2  9.16 

Crusader..". «  16.8  11.8  9.3 

Wyandotte Yer.  water-tubes 20  12.4  10 

Underwriter Hor.  flue  boiler 15.6  11.2  9.9 

Young  America..         "  "     15  10.4  9.3 

Boston,  of  K  Y. .  Marine  tubular 18  11.1  11.5 


10.2 

1st  column. — Heating-surface  required  per  indicated  PI.  P. 

2d  column. — Water  evaporated  per  hour  per  pound  of  com- 
bustible. 

3d  column. — Combustible  in  pounds  burned  per  hour  per 
square  foot  of  grate. 

The  practice  of  the  Navy  Department,  according  to  the  com 
mittee,  is  to  allow  8  pounds  of  anthracite  coal  per  hour  to 
evaporate  1  cubic  foot  of  water  at  212°,  under  a  pressure  of  30 
pounds  per  square  inch,  which  requires  -f  square  foot  of  grate 
and  16f  square  feet  of  heating-surface. 

If  the  evaporative  powers  of  different  boilers  be  referred  to 
the  heating-surface,  it  will  be  found  that  the  quantity  evapora- 
ted for  each  square  foot  of  heating-surface  of  the  plain  cylin- 
der boiler  appears  greatly  in  excess  of  the  quantity  evaporated 


THE  CONSTRUCTION  OF  STEAM  GENERATORS.  161 

by  one  square  foot  of  heating-surface  of  the  flue  and  tubular 
boilers.  In  the  plain  cylinder  boiler  the  heating-surface  is 
universally  estimated  by  taking  the  lower  half  of  the  shell  only, 
as  this  is  the  only  part  exposed  to  heat.  But  it  would  un- 
doubtedly be  more  in  accordance  with  the  process  of  the  trans- 
fer of  heat  to  add  to  the  heating-surface  the  bottom  of  the  flue 
beyond  the  furnace  that  leads  to  the  chimney,  because  this 
becomes  intensely  heated  and  must  give  off  by  radiation  to  the 
opposite  surface  nearly  as  much  heat  as  the  latter  receives  by 
the  direct  contact  of  the  gases.  So  also  with  all  internal  as 
well  as  external  fire -flues,  the  total  internal  surfaces  should  be 
considered  as  heating-surfaces,  though  not  technically  answer- 
ing to  the  definition  in  all  cases.  If  this  principle  be  adopted, 
the  heating-surface  of  the  plain  cylinder  boiler,  and  of  all  ex- 
ternal furnace  boilers,  will  have  the  same  value  as  other  heat- 
ing-surfaces, and  the  evaporation  per  square  foot  of  heating- 
surface  will  correspond,  nearly,  for  all  boilers  which  have  the 
same  amount  of  heating-surfaces  and  rates  of  combustion,  and 
the  ratio  of  heating-surface  to  the  grate-surface  will  approach 
uniformity  for  all  boilers  for  the  same  rates  of  combustion. 

For  example,  the  rate  of  evaporation  of  plain  cylinder, 
cylinder  flue,  and  cylinder  tubular  boilers,  per  square  foot  of 
heating-surface,  is  in  practice  according  to  the  present  modes 
of  estimating  heating-surface : 

Plain  cylinder  boilers 6.4  Ibs.  of  water  per  hour. 

Cylinder  flue  boilers 4.8         "         "         « 

Cylinder  tubular  boilers..   4.3         "         "         " 

If  now  we  add  for  the  plain  cylinder  boilers  and  return-flue 
and  tubular  boilers,  to  the  heating-surface  estimated  in  the  usual 
way,  the  additional  radiating  surface  of  the  bottom  of  the 
external  flue,  we  shall  have  for  each  of  these  three  external 
furnace  boilers,  a  rate  of  evaporation  per  square  foot  of  heating- 
surface  approximately  equal  to  4.0  pounds  of  water  per  hour. 

The  extent  of  heating-surface  is  still  practically  less  for  the 
plain  cylinder  than  for  the  others,  and  it  is  for  this  reason  less 
efficient. 

The  quantity  of  water  evaporated  per  pound  of  coal  for  each  of 
these  three  boilers  in  the  order  given  is,  under  the  most  favorable 
circumstances,  7,  8,  and  9  pounds  of  water  for  each  pound  of 
coal  burned,  and  these  figures  will  represent,  according  to  the 


162  THE  CONSTRUCTION  OF  STEAM  GENERATORS. 

method  proposed,  the  relations  of  the  heating-surfaces  in  each 
for  the  same  rates  of  combustion. 

The  railroad  locomotive  is  the  only  boiler  in  which  the  rates 
of  combustion  are  frequently  and  greatly  varied  while  in  use, 
and  in  these  boilers  it  is  necessary  to  provide  for  very  high  rates 
of  combustion  by  giving  an  extreme  amount  of  heating-surface. 

The  locomotive  boiler,  with  ordinary  rates  of  combustion, 
corresponds,  in  evaporative  efficiency,  to  the  ordinary  marine 
tubular  boiler. 

The  following  results  on  the  evaporative  efficiencies  of  the 
sectional  boilers  are  from  the  report  of  the  committee  appoint- 
ed by  the  American  Institute,  to  which  reference  has  been  made. 

237.  Hoot  Boiler. — Grate  surface,  27 ;  ratio  of  heating-sur- 
face to  grate,  32.5  to  1 ;  coal  burned  per  hour  per  square  foot 
of  grate,  11.73  pounds.     Actual  evaporation  per  pound  of  coal, 
7.34  pounds  of  water ;  per  pound  of  combustible,  8.76  pounds ; 
equivalent  evaporation  at  212°,  10.64  pounds. 

238.  Allen  Boiler. — Grate,  32J  square  feet ;  ratio  of  heating- 
surface  to  grate-surface,  28.5  ;  coal  burned  per  hour  per  square 
foot  of  grate,  13.88  -pounds.    Actual  evaporation  at  75  pounds 
per  pound  of  coal,  7.38  pounds  of  water ;  actual  evaporation 
per  pound  of  combustible,  8.76  ;  equivalent  evaporation  at  212° 
F.,  10.60  pounds  of  water. 

239.  Phleger  Boiler. — Grate,  23  square  feet ;  ratio  of  heating- 
surface  to  grate,  26.1  to  1 ;  coal  burned  per  square  foot  of  grate- 
surface,  10.13  pounds ;  actual  evaporation  at  75  pounds  pressure 
per  pound  of  coal,  7.07 ;  actual  evaporation  per  pound  of  combus- 
tible, 8.70 ;  equivalent  evaporation  at  212°  F.,  10.49  pounds  of 
water.     The  amount  of  heating-surface  necessary  to  evaporate 
1  cubic  foot  of  water  per  hour  in  these  boilers  was  respectively 
23.59,  17.41,  and  22.74  square  feet. 

240.  Causes  which  affect  the  efficiency  of  evaporation. — These 
are,  1st,  those  which  influence  the  rate  of  combustion,  and,  2d, 
those  which  influence  the  rate  of  transfer  of  heat. 

Among  the  causes  which  influence  the  rate  of  combustion 
may  be  mentioned — 

The  temperature  of  the  external  air. 

The  temperature  of  the  chimney  gases. 

The  presence  of  moisture  in  the  air. 

The  management  of  the  fires,  the  quality  of  the  fuel,  and 
defective  combustion. 


THE  CONSTRUCTION  OF  STEAM  GENERATORS.          163 

The  principal  causes  which  affect  the  transfer  of  heat  are — 

The  rate  of  combustion,  which  determines  the  initial  tem- 
peratures in  the  "boiler. 

The  temperature  of  the  water  in  the  boiler. 

The  accumulations  of  incrustations  and  dust  in  the  tubes,  and 
generally  all  those  circumstances  which  impair  the  qualities 
of  the  heating-surfaces. 

The  influence  of  the  external  temperature  and  of  the  baro- 
metric pressure  on  the  rate  of  combustion  cannot  well  be  esti- 
mated. An  increased  density  of  the  external  air  favors  com- 
bustion by  increasing  the  draft,  and  also  because  a  less  volume 
of  cooler  air  is  necessary  to  burn  one  pound  of  combustible. 
The  draft  of  chimneys  is  thus  rendered  more  active  in  winter 
than  in  summer. 

The  influence  of  the  internal  temperature  of  the  gases  has 
less  effect.  It  is  pointed  out  by  Peclet  that  the  maximum  draft 
occurs  only  with  an  infinite  degree  of  temperature  in  the  chim- 
ney, but  that  a  temperature  of  about  600°  F.  gives  -^  of  the 
maximum. 

The  statement  in  Kankine  that  the  maximum  quantity  of  air 
drawn  in  occurs  for  a  temperature  of  the  heated  gases  of  about 
600°  F.  seems  to  be  an  error,  as  no  such  theoretical  maximum 
exists  in  the  formula  for  draft  that  has  been  given. 

The  influence  of  the  moisture  in  the  atmosphere  is  often  im- 
portant. In  proportion  as  the  moisture  in  the  air  augments, 
the  fires  languish,  especially  with  a  feeble  pressure — a  dry, 
cold  air,  with  a  high  barometer,  being  more  favorable  to  com- 
bustion. It  is  stated  by  Peclet  that  in  many  of  the  glass  facto- 
ries of  France  work  is  suspended  in  summer  on  this  account. 

The  management  of  the  fires  and  the  quality  of  coal  is  one  of 
the  most  important  influences  on  the  rate  of  combustion  and 
economy  of  fuel.  It  is  stated  by  Morin  and  Tresca  that  the 
Industrial  Society  of  Mulhouse  offered  a  reward  of  five  silver 
medals,  and  three  sums  of  money,  to  the  stokers  who  should 
show  themselves,  in  a  competitive  trial,  the  most  skilful  in 
the  management  of  the  fires  of  a  boiler.  The  results  showed 
a  difference  of  13  per  cent,  in  the  extremes  of  the  quantities  of 
water  evaporated  under  conditions  precisely  similar.  If  this 
difference  could  occur  in  a  trial  between  stokers  of  acknowl- 
edged skill,  what  must  be  the  effect  of  ignorance  and  careless- 
ness combined  ? 


164          THE  CONSTRUCTION  OF  STEAM  GENERATORS. 

241.  Of  the  causes  which  affect  the  transfer  of  heat,  and  thus 
affect  the  rate  of   evaporation,  the  rate  of  combustion  has  an 
effect  which  gives  rise  to  an  increased  rate  for  high  rates  of 
combustion  with  the  same  heating-surface.     The  same  amount 
of  heat  is  evolved  whether  the  rate  of  combustion  be  slow  or 
rapid ;  but  to  prevent  loss  additional  heating-surface  is  requir- 
ed for  high  rates  of  combustion.     It  is  necessary  to  distinguish 
between  the  rate  of  evaporation  for  a  given  heating-surface 
and  the  total  heat  evolved  and  transferred. 

In  order  that  no  loss  shall  occur,  it  is  necessary  that  the 
heated  gases  should  always  enter  the  chimney  with  the  least 
practicable  temperature. 

The  condition  of  the  heating-surfaces  is  a  matter  of  impor- 
tance in  connection  with  the  rate  of  evaporation.  Internal  de- 
posits of  all  kinds,  whether  from  incrustation  or  from  the 
accumulation  of  dirt,  cause  a  loss  of  heat,  as  well  as  the  de- 
struction of  the  heating-surfaces ;  new  boilers  are,  for  these 
reasons,  more  efficient  than  old  ones. 

The  effect  of  the  pressure  in  the  boiler  is  very  slight.  There 
is  some  loss  in  the  rate  of  transfer  as  the  pressure  is  increased, 
owing  to  the  fact  that  the  temperature  of  the  absorbent  is  in- 
creased, and  the  rapidity  of  transfer  depends  on  the  difference 
between  the  temperatures  of  the  source  and  the  absorbent. 
It  is  impossible  to  estimate  this  loss,  which  is,  however,  only 
slight.  As  to  the  quantity  of  heat  necessary  to  evaporate 
water  at  different  temperatures,  the  total  heat  required  in- 
creases slightly  with  the  temperature,  but  the  increase  is  insig- 
nificant ;  the  difference  between  1  and  6  atmospheres  being 
only  about  .02  of  the  total  amount. 

242.  In  regard  to  the  mode  of  estimating  heating-surfaces, 
there  has  been  a  great  deal  of  uncertainty,  and  great  diversity 
of  practice.     A  portion  of  the  heating-surface  is  exposed  to  the 
direct  radiation  of  the  grate,  and  at  the  same  time  to  the  con- 
tact of  the  heated  gases  at  their  initial  temperature  ;  and  some 
engineers,  for  this  reason,  divide  the  heating-surface  into  two 
parts, ,  direct  and  indirect  heating-surfaces.     The  direct  heat- 
ing-surfaces   bear  to    the    total   heating-surfaces    proportions 
which  differ  in  the  different  types.     In  the  locomotive,  for  in- 
stance, it  is  about  ^.of  the  whole;  in  marine  boilers,  about  i; 
in  cylinder-tubular  and  flue  boilers  from  \  to  \. 

There  is  no  doubt  that  the  direct  heating-surface  is  the  most 


THE  CONSTRUCTION  OF  STEAM  GENERATORS.  165 

efficient,  since  the  quantity  of  heat  transferred  by  direct  radia- 
tion in  a  given  time,  from  one  square  foot  of  surface,  with 
a  given  difference  of  temperature,  for  the  great  differences 
which  occur  in  boilers,  is  much  mare,  probably  6  to  8  times 
more,  than  the  quantity  transferred  by  contact  of  the  gases  for 
the  mean  temperatures  of  the  Hues.  But  it  is  impossible  to 
separate  these  influences,  and  it  accords  with  the  best  practice 
to  consider  the  heating-surface  as  a  whole. 

There  seem  to  be  stronger  objections  still  to  an  arbitrary  divi- 
sion of  the  surfaces  of  flues  into  parts  of  greater  or  less  efficiency, 
when  there  is  no  possibility  of  ascertaining  the  value  of  those 
parts  as  regards  efficiency,  and  especially  as  there  appears  to 
be  actual  misapprehension  in  regard  to  the  action  of  these  sur- 
faces. 

If  the  under-side  of  a  flue  is  to  be  left  out  of  consideration, 
the  question  may  be  asked,  what  becomes  of  the  heat  trans- 
ferred to  it ;  for  there  must  be  heat  transferred  to  it  by  contact 
of  the  gases.  There  is  no  doubt  that  the  overheating  is  pre- 
vented in  part  by  radiation  across  the  flue  to  the  opposite  side, 
and  this  radiation  tends  to  equalize  the  temperature  of  the  flue 
around  its  entire  circumference.  For  similar  reasons  the  outer 
surfaces  of  external  flues  should  be  taken  into  account.  The 
contact  of  the  heated  gases  would  otherwise  heat  the  sides  of 
the  external  flues  to  a  red-heat  nearly,  and  such  a  heated  sur- 
face near  a  flue,  it  must  be  acknowledged,  would  radiate  heat 
rapidly  across  the  space  which  separates  it  from  the  metallic 
plate  of  the  boiler. 

It  seems,  therefore,  advisable  to  estimate  all  surfaces  of  flues, 
both  of  external  and  internal  flues,  as  heating-surfaces.  Some 
of  the  anomalies  in  regard  to  the  efficiency  of  heating-surfaces 
would  then  disappear. 

243.  Proportions  of  Water-room  and  Steam-room. — The 
total  internal  volume  of  a  steam  generator  may  be  divided  into 
two  parts,  that  which  is  ordinarily  occupied  by  water  and  that 
which  is  occupied  by  steam. 

It  has  been  customary  in  England  to  fix  the  volume  of  steam- 
room  at  ten  cubic  feet  for  each  cubic  foot  of  water  vaporized 
per  hour.  This  proportion  is  based  on  the  idea  that  a  certain 
reserve  of  steam  is  desirable  in  proportion  to  the  water  evapo- 
rated per  hour.  The  proportion  seems  unnecessarily  great  un- 
less the  steam-dome  is  included.  Without  the  steam-dome  a 


166          THE  CONSTRUCTION  OF  STEAM  GENERATORS. 

proportion  of  five  cubic  feet  for  each  cubic  foot  of  water  eva- 
porated per  hour  accords  more  nearly  with  practice.  Accord- 
ing to  Bourne,  the  water-room  should  be  three-fourths  and  the 
steam-room  one-fourth  of  the  whole  internal  capacity.  Arm- 
strong recommends  equal  proportions  of  water-room  and  steam- 
room.  The  proportions  should  be  in  reality  different  for  differ- 
ent boilers.  For  land  boilers,  three-fourths  water-room  and  one- 
fourth  steam-rooin  may  be  regarded  as  a  good  proportion.  For 
marine  boilers,  nearly  equal  proportions,  and  for  locomotives 
about  two-thirds  water-room  and  one-third  steam-room  may  be 
taken  as  average  proportions. 

244.  Priming. — Priming  consists  in  the  carrying  of  particles 
of  water,  mechanically,  into  the  delivery  pipes  of  a  boiler,  and 
thence  into  the  cylinder  of  the  engine  (where  an  engine  receives 
the  steam),  and  is   caused  principally   by    deficiency   of  the 
steam-room ;  or,  at  least,  a  deficiency  of  the  free  surface,  or 
water-level.     It  is  also  caused  by  impurities  in  the  water.    The 
provision  of  a  large  steam-space,  especially  where  there  is  a 
limited  free  surface,  is  therefore  important,  to  prevent  priming. 

The  effect  of  an  over-full  boiler  in  causing  excessive  priming 
is  a  matter  of  common  observation. 

245.  Proportions  of  the  furnace. — The  height  of  the  crown 
of  the  furnace  above  the  grate-bars  is  seldom  less  than  eighteen 
inches,  even  in  small  boilers,  and  should  always  be  greater  than 
this  if  practicable.     In  locomotive  boilers  this  height  is  gener- 
ally about  four  feet.     A  high  furnace  is  favorable  for  complete 
combustion.     The  height  is  limited  practically,  in  boilers  which 
have  return-tubes  or  flues,  by  the  necessity  for  having  sufficient 
depth  of  water  above  the  crown  to  cover  them.     In  marine  and 
land  boilers  ten  to  twelve  inches'  depth  over  the  flues  is  advisa- 
ble ;  in  locomotive  boilers,  five  to  six  inches. 

246.  Actual  Dimensions. — In  deciding  upon  the  actual  dimen- 
sions of  a  steam  generator,  required  for  a  special  purpose,  the 
engineer  is  supposed  to  know  the  quantity  of  steam  required  per 
hour  and  the  pressure  at  which  it  is  to  be  produced. 

The  quantity  may  be  given  in  cubic  feet  or  i»  pounds,  and 
the  volume  or  weight  required  for  any  given  pressure  may  be 
found  from  the  table  in  this  work  which  gives  the  specific  vol- 
umes or  specific  weights,  page  63.  The  weight  of  steam  used 
per  hour  is  always  sensibly  equal  to  the  weight  of  water  evapo- 
rated, and  a  boiler,  or  set  of  boilers,  is  to  be  chosen  which  will 


THE  CONSTRUCTION  OF  STEAM  GENERATORS.  167 

evaporate  the  required  quantity  of  water  per  hour.  From  what 
precedes,  it  may  be  assumed  that  the  problem  of  actual  dimen- 
sions is  indeterminate  without  some  other  specifications  than  the 
quantity  of  steam  required  and  the  pressure,  because  there  may 
be  any  number  of  boilers  of  different  dimensions  that  will  an- 
swer the  purpose.  To  illustrate :  let  it  be  required  to  construct  a 
tubular  boiler  that  will  evaporate  5,000  Ibs.  of  water  per  hour, 
at  any  given  pressure.  If  we  suppose  the  boiler  to  be  furnished 
with  a  steam  jet,  by  which  a  rate  of  combustion  of  60  Ibs.  of 
coal  per  hour  for  each  square  foot  of  grate  may  be  attained, 
each  lb.  of  coal  will  evaporate  about  7  Ibs.  of  water,  if  the  heat- 
ing-surface bears  the  proportion  of  70  to  1  of  grate ;  12  feet 
of  grate-surface  and  840  of  heating-surface  will  then  be  approxi- 
mately the  elements  which  will  determine  the  actual  dimen- 
sions. If  the  boiler,  on  the  other  hand,  is  to  be  attached  to  a 
chimney,  with  such  a  draft  that  only  12  Ibs.  of  coal  will  be 
burned  in  an  hour  011  each  square  foot  of  grate-surface, 
each  pound  of  coal  will  evaporate  about  9  Ibs.  of  water,  if  the 
boiler  be  supplied  with  25  square  feet  of  heating-surface  to  1 
square  foot  of  grate-surface.  Under  these  conditions  48  square 
feet  of  grate-surface  and  1150  feet  of  heating-surface  will  deter- 
mine the  dimensions  approximately. 

In  the  first  case,  60  x  12  x  7=5040,  and  in  the  second,  48  x  12 
X  9 =5184  pounds  of  water  will  be  evaporated.  Any  number 
of  different  combinations  might  thus  be  found,  each  of  which 
would  accomplish  the  same  result.  The  considerations  which 
influence  a  choice  may  be  derived  from  an  examination  into 
these  two  cases  in  detail. 

In  the  first  case,  720  pounds  of  coal  are  required  to  evapo- 
rate 5040  pounds  of  water  in  an  hour ;  and  in  the  second,  576 
pounds  of  coal ;  the  difference,  148  pounds,  being  the  amount 
of  coal  in  favor  of  the  slower  combustion  and  larger  grate-sur- 
face. The  boiler  of  large  capacity  has  the  advantage,  also,  in 
steadiness  of  pressure,  freedom  from  priming,  and  space  for  the 
collection  of  sediment ;  moreover,  the  durability  of  boilers  is 
greater  when  the  apparatus  is  subjected  to  less  extremes  of  heat. 
The  points  in  favor  of  the  smaller  capacity  are,  rapid  raising  of 
steam,  small  surface  for  waste  heat,  economy  of  space  and  of 
weight,  and  greater  strength  with  a  given  quantity  of  material. 

For  a  portable  boiler  the  least  weight  is  desirable,  and  a  high 
rate  of  combustion,  even  with  a  sacrifice  of  economy  of  fuel, 


168  THE  CONSTRUCTION  OF  STEAM  GENERATORS. 

may  be  preferred.  On  the  other  hand,  if  a  chimney-draft  is 
employed  for  the  combustion,  an  excessive  rate  can  only  be  at- 
tained by  a  very  high  chimney,  which  involves  extraordinary 
expense. 

These  considerations  are  sufficient  to  show  the  various  grounds 
of  choice. 

Generally  these  are  sufficiently  fixed  by  circumstances  of 
use.  For '  marine  purposes,  for  instance,  economy  of  fuel 
is  of  the  greatest  importance,  especially  as  all  the  fuel  for 
a  voyage  must  be  carried  from  the  point  of  departure. 
Steadiness  of  pressure  and  supply  of  steam  are  also  important. 
The  chimney  is  in  this  case  the  ordinary  means  of  draft  (the 
exhaust-steam  being  usually  condensed),  and  it  is  necessary  to 
keep  the  chimney  as  low  as  possible.  All  these  considerations 
tend  to  fix  the  conditions  for  marine  boilers,  and  hence  the  rule 
given  in  a  preceding  paragraph  as  to  the  practice  of  the  U.  S. 
Navy  Department  for  heating-surface  and  grate-surface.  In 
railroad  locomotives,  on  the  other  hand,  the  least  weight  prac- 
ticable is  desired,  and  the  loss  of  economic  effect  in  fuel  is 
more  than  counterbalanced  by  the  saving  effected  by  the  lesser 
load  to  be  transported.  For  land  boilers,  with  chimney-draft, 
the  heights  of  chimneys  are  such  as  to  cause  a  combustion  of  12 
to  18  pounds  of  coal  per  hour  on  each  square  foot  of  grate. 
Here  there  is  occasion  for  discrimination,  and  the  amount  of 
grate-surface  should  be  first  determined  from  the  probable  rate 
of  combustion,  and  the  total  quantity  of  combustible  required 
per  hour  to  evaporate  the  required  quantity  of  water.  The 
grate-surface  having  been  thus  estimated,  the  other  dimensions 
will  follow  from  the  proper  proportions  applicable. 

It  is  hardly  necessary  to  state,  after  what  precedes,  that  the 
inverse  problem  is  equally  dependent  on  the  conditions  which 
have  been  enumerated. 

For  example,  having  a  given  boiler,  to  ascertain  what  quan- 
tity of  water  can  be  evaporated  by  it  in  an  hour,  it  is  neces- 
sary to  know  the  quantity  of  coal  burned  per  hour,  or  rate  of 
combustion,  for  each  square  foot  of  grate-surface,  and  also  the 
quantity  of  heating-surface,  in  order  that  the  quantity  of  water 
evaporated  by  each  pound  of  coal  per  hour  may  be  determined. 

247.  Efficiency  of  Steam  Generators. — By  efficiency  is  to  be 
understood  the  quantity  of  heat  transferred  to  the  water,  in 
proportion  to  the  total  quantity  evolved  by  the  combustion. 


THE  CONSTRUCTION  OF  STEAM  GENERATORS.          169 

The  total  heat  of  combustion  of  one  pound  of  coal  is  sufficient 
to  evaporate  about  15  pounds  of  water,  the  water  being  sup- 
plied and  evaporated  at  212°  Fahr. 

The  ordinary  evaporation  is,  as  has  been  shown,  from  7  to  9 
pounds  in  current  practice.  The  efficiency  will  be  J^-  to  T9y. 
The  differences  between  7  and  15  or  9  and  15  (round  numbers 
being  given),  will  represent  in  each  case  the  waste  heat  and  the 
heat  required  to  produce  the  draft,  where  there  is  a  simple 
chimney  draft;  in  other  cases  the  waste  heat  alone. 

The  waste  heat  arises  from  several  causes  :' 

1.  Waste  of  unburnt  fuel  in  the  solid  state. 

2.  Waste  of  unburnt  fuel  in  the  gaseous  or  smoky  state. 

3.  Waste  by  external  radiation  and  conduction. 

4.  Waste  by  the  excess  of  heat  which  escapes  by  the  chim- 

ney, over  that  required  for  the  draft. 

These  sources  of  waste  may  give  rise  to  excessive  losses  which 
perfect  arrangements  and  good  management  are  intended  to 
avoid.  If  the  arrangements  and  proportions  adopted  by  the 
engineer  are  suitable,  the  stoker  is  generally  responsible  for  a 
large  part  of  the  waste  which  may  occur  in  the  combustion. 

An  excessive  quantity  of  coal  in  small  unburnt,  or  partially 
burnt,  pieces  in  the  ash-pit,  is  evidence  of  direct  carelessness  or 
inattention.  Irregular  and  excessive  charges,  especially  when 
attended  by  irregular  cleaning  of  the  grate,  are  very  sure  to 
cause  waste,  through  the  chimney,  of  combustible  gases  and 
smoke.  The  waste  by  radiation  and  conduction  is  to  be  pre- 
vented as  much  as  possible  by  proper  non-conducting  and  non- 
radiating  materials,  such  as  felting  for  the  covering  of  the 
shell,  or  brick  chambers  enclosing  the  boiler.  Waste  by  exces- 
sive heat  in  the  chimney  ought  not  to  occur  when  there  is  suffi- 
cient heating- surf  ace,  and  when  the  heating-surfaces  are  kept 
in  good  condition. 

The  accumulation  of  internal  deposits  and  incrustations,  how- 
ever, often  causes  a  steady  diminution  of  efficiency  in  boilers 
which  are  constantly  in  use ;  a  diminution  which  cannot  be 
prevented. 

In  furnaces  in  which  the  draft  is  produced  by  a  blast,  or 
fan,  all  the  heat  which  passes  through  the  chimney  must  be 
considered  as  waste. 

In  regard  to  the  amount  of  these  different  elements  of  waste, 
it  may  be  said  that  the  loss  from  the  occurrence  of  unburnt 


170          THE  CONSTRUCTION  OF  STEAM  GENERATORS. 

combustible  in  the  ash-pit  may  be  in  some  degree  prevented  by 
a  careful  sifting  or  raking  of  the  ashes.  Some  ashes  contain 
large  quantities  of  coke,  besides  small  pieces  of  unburnt  coal, 
which  can  be  saved. 

The  waste  by  the  escape  of  combustible  gas  (carbonic  oxide) 
may  amount  to  one-tenth  of  the  whole  heat. 

The  amount  of  heat  lost  by  the  high  temperature  of  the 
escaping  gases  depends  not  only  on  the  temperature  of  the 
escaping  gases,  but  also  on  the  quantity  of  air  admitted  for 
each  pound  of  coal  burned.  Where  an  excessive  quantity  of 
air  is  admitted,  and  a  high  temperature  prevails  in  the  chimney, 
the  loss  may  be  very  great.  The  most  favorable  conditions  are 
when  the  quantity  of  air  admitted  is  just  sufficient  for  combus- 
tion, and  the  heat  of  the  chimney  just  sufficient  to  produce  the 
draft. 

The  most  unfavorable  circumstances  which  can  ordinarily 
occur  are  those  in  which  the  quantity  of  air  admitted  is  about 
three  times  the  theoretical  quantity  (the  initial  temperature  of 
the  gases  consequently  low),  and  when  the  temperature  of  the 
chimney  gases  is  high. 

It  is  impossible  to  estimate  the  loss  of  heat  by  radiation  and 
conduction  through  the  masonry,  by  the  entrance  of  air 
through  joints  into  the  tubes  and  chimney,  and  by  radiation 
from  the  shell ;  but  it  is  certain  that  these  causes  of  loss  are 
such  that  it  is  important  to  prevent,  by  the  most  efficacious 
means  practicable,  all  access  of  air,  except  at  the  points  where 
it  is  needed  for  combustion,  and  to  guard  against  loss  by  con- 
duction and  radiation  by  proper  non-conducting  materials  and 
arrangements  for  the  furnace,  the  flues,  and  for  the  shell. 

The  efficiencies  stated  above  are  by  no  means  the  highest  that 
ought  to  be  attained,  nor  are  they  the  lowest  that  probably 
occur  in  most  manufacturing  establishments.  There  is  no 
doubt  that  a  saving  of  20  per  cent,  and  often  30  per  cent,  of 
the  quantities  of  coal  now  consumed  in  many  manufacturing 
establishments  might  be  effected  by  the  introduction  of  more 
perfect  proportions  and  arrangements,  and  especially  by  the 
employment  of  thoroughly  skilled  and  intelligent  stoJcers. 
There  is  greater  prospect  and  room  for  improvements  in  these 
respects  than  through  any  new  inventions  or  devices  for  boilers. 

248.  Horse-power  of  J3  oilers. — The  term  horse-power  can 
hardly  be  applied  with  propriety  to  steam  generators,  inasmuch 


THE  CONSTRUCTION  OF  STEAM  GENERATORS.          171 

as  it  implies  a  rate  of  work,  and  a  boiler  ordinarily  does  no 
work,  but  merely  supplies  the  means  of  work  to  a  machine. 
The  amount  or  rate  of  work  is  thus  dependent  on  the  utilization 
of  the  sjeam,  and  must  vary  with  the  variations  of  the  ma- 
chine which  utilizes  it.  Moreover,  the  application  of  this 
term  to  boilers  is  especially  inappropriate  when  it  is  determined 
solely  by  the  dimensions  of  the  boiler,  as  is  usually  the  case  ;  a 
boiler  of  certain  dimensions  being  spoken  of  as  a  boiler  of  10- 
horse  power,  another  of  larger  dimensions  as  one  of  20-horse 
power,  etc.  In  reality,  a  boiler  called  a  10-horse-power  boiler 
may,  according  to  any  rational  rule  which  can  be  adopted,  be 
made  a  20-horse-power  boiler  by  simply  increasing  the  rate  of 
combustion,  or  the  pressure  of  the  steam,  or  both  combined. 
A  railroad-locomotive  boiler,  for  example,  in  the  course  of  a 
single  trip  may  vary  extremely  in  these  particulars,  and  will  at 
one  time  produce  steam  in  large  quantities  under  high  degrees 
of  pressure,  and  at  another  greatly  reduced  quantities  of  steam 
under  reduced  pressures ;  and  yet,  according  to  the  current 
ideas  of  horse-power  of  boilers,  it  would  all  the  time  be  a  boiler 
of  a  fixed  horse-power. 

This  becomes  a  matter  of  some  importance  when  boilers  are 
bought  and  sold  according  to  their  horse-power,  because  in  case 
of  dispute  it  is  impossible  to  attach  definite  ideas  to  the  terms 
employed,  unless  it  be  at  the  same  time  specified  what  is  to  be 
the  rate  of  combustion,  and  the  pressure.  The  rate  of  com- 
bustion is  subject  to  such  variable  conditions  that  it  is  difficult 
to  establish  it  precisely,  and  the  custom  of  describing  the  ca- 
pacity of  boilers  by  the  term  horse-power  is,  therefore,  liable  to 
lead  to  difficulty. 

It  may  be  desirable,  however,  to  have  a  standard  for  the 
capacity  of  boilers  in  order  to  compare  the  work  actually 
accomplished,  under  different  circumstances  by  the  steam  fur- 
nished, with  this  standard.  The  maximum  quantity  of  work 
which  the  steam  from  a  boiler  is  capable  of  exerting,  for  a 
given  rate  of  evaporation  and  a  given  pressure,  in  a  perfect 
engine,  may  easily  be  found  ;  a  perfect  engine  in  this  respect 
being  one  in  which  there  is  no  clearance,  and  in  which  the 
pressure  of  the  steam  is  the  same  as  that  in  the  boiler,  the  coun- 
ter-pressure being  the  pressure  of  the  atmosphere  or  of  the  con- 
denser, and  the  pressure  diminishing  by  the  expansion  from 
that  of  the  boiler  to  that  of  the  atmosphere  or  condenser ;  and 


172 


THE  CONSTRUCTION  OF  STEAM  GENERATORS. 


finally,  no  resistance  being  offered  to  the  flow  of  steam  through 
the  pipes  and  valves.  Such  an  engine  cannot  be  constructed, 
but  is  theoretically  supposable. 

The  quantities  of  water  or  steam,  in  pounds,  required  to  pro- 
duce one  horse-power  per  hour  for  non-condensing  and  con- 
densing engines  under  these  circumstances,  for  different  pres- 
sures, is  as  follows  (the  figures  being  taken  from  Professor 
Zeuner's  work  on  the  mechanical  theory  of  heat,  English  meas- 
ures being  substituted) : 


Pounds  of  Water  per  Horse-Power 

per  Hour. 

Tension  of  Vapor  in 

Atmospheres. 

Non-condensing 

Condensing 

Engine. 

Engine. 

it 

72.9 

15.6 

3 

32.8 

12.7 

4 

26.3 

11.8 

5 

22.9 

11.3 

6 

20.7 

10.8 

8 

18.0 

10.3 

10 

16.5 

9.9 

If  we  take  as  the  standard  the  perfect  non-condensing  engine, 
the  available  capacity  of  the  steam  for  any  boiler  may  be  found 
in  horse-power  by  dividing  the  number  of  pounds  of  water 
evaporated  per  hour,  at  a  given  pressure,  by  the  number  of  this 
table  for  the  same  pressure  in  the  second  column.  Another 
method  may  be  derived  from  calculations  based  upon  the  living 
force  of  steam  issuing  from  an  orifice  in  a  boiler  into  the  atmos- 
phere. 

The  velocity  of  efflux  being  independent  of  the  area  of  the 
orifice,  we  may  also  suppose  it  to  be  uninfluenced  by  friction  or 
other  resistances.  Under  these  circumstances  the  theoretical 
velocity  may  be  found  for  different  internal  pressures,  and  a 
constant  external  atmospheric  pressure.  It  is  evident  that  when 
the  size  of  the  orifice  is  such  that  the  whole  work  of  the  boiler 
consists  in  forcing  into  the  atmosphere  the  steam  generated,  if 


THE  CONSTRUCTION  OF  STEAM  GENERATORS.  173 

w  be  the  weight  of  steam  generated  in  a  minute,  the  work  per 


*w  v  2 


minute  will  be  equivalent  to  —  —  ,  and  the  number  of  fiorse- 

' 


2  g 

W  V 


2  g  33,000- 

The  following  theoretical  velocities  are  taken  from  Professor 
Zeuner's  work  : 


Pressures  in  the  Boiler.  Velocities  in  Metres 

Atmospheres.  per  Second. 

2 481.71 

3 606.57 

4 681.48 

5 734.32 

6 774.89 

7 807.57 

8 834.90 

9 858.33 

10..  ..878.74 


For  these  velocities  the  values  of  ^ —     nnA,  found  for  the  same 

g  oOjUUU 
pressures  respectively,  are : 

w  —  number  of  horse-power. 


.Pressures  in 
Atmospheres. 

2  

1.11  x 

3... 

1  87  " 

4  

.  .  2.34  " 

5  

..2.75  " 

6  

3.07  " 

7  

.   3  35  " 

8  

..3.58  " 

9  

.  .  3  80  " 

10.. 

..3.95  " 

The  numbers  of  this  table  multiplied  by  the  quantity  of 
water,  in  pounds,  evaporated  per  minute  will  give  the  horse- 
power of  the  boiler,  when  it  performs  the  work  of  forcing 
steam  into  the  atmosphere  under  the  conditions  stated. 

These  two  methods,  though  accomplished  by  different  pro- 


THE  CONSTRUCTION  OF  STEAM  GENERATORS. 


cesses,  should  give  identical  results.  It  was  pointed  out  by 
Professor  Zeuner  that  the  living  force  of  steam  issuing  from  a 
boiler,  under  the  circumstances  mentioned,  is  equivalent  to  the 
work  performed  by  the  steam  in  a  perfect  engine,  equal  quan- 
tities being  considered. 

The  actual  work  of  ordinary  steam-engines  falls,  of  course, 
much  below  the  theoretical,  the  efficiency  depending  upon  the 
approximation  to  the  perfect  conditions  already  named. 

The  quantities  of  water  actually  required  in  practice  for  one 
horse-power  per  hour,  in  small  non-condensing  engines  working 
under  the  most  favorable  degrees  of  expansion  practicable,  are 
approximately  as  given  below : 


TABLE  XXX. 

Experimental  and   Theoretical  Quantities  of   Water  required  in  Non-con- 
densing Engines  for  one  Horse-power  per  Hour. 


Results  of  Experiments 
on  small  Engines  by 
Mr.  C.  E.  Emery. 

Theoretical 
Quantities. 

Pressure  of 
Steam  in 
Pounds. 

Water  required  per 
Horse-power  per 
Hour  in  Pounds. 

Water  required  per  Horse- 
power per  Hour  in 
Pounds.           •    ' 

30 

56 

58 

35 

51 

45 

40 

48 

37 

45 

45 

32.5 

50 

43 

29.5 

55 

41 

27.5 

60 

39 

26 

70 

37 

23 

80 

34 

21.5 

90 

32 

20.3 

100 

31 

19.5 

The  above  results  of  experiments  are  probably  near  the  high- 
est limits  of  economy  attainable  for  the  different  pressures 
given,  and  the  numbers  in  the  second  column  represent  the 


THE  CONSTRUCTION  OF  STEAM  GENERATORS.          175 

lowest  quantities  of  water  ordinarily  reached  in  practice  with 
small  engines  for  the  production  of  one  horse-power  per  hour. 
The  theoretical  results  in  the  third  column  are  for  a  theoreti- 
cally perfect  non-condensing  engine. 

Suppose  now  a  boiler  to  evaporate,  at  100  Ibs.  pressure,  3,000 
pounds  of  water  per  hour,  the  horse -power  of  the  boiler  will  be, 

according  to  table,  ?^  x  3.27  =  163.5  H.  P. 

The  actual  performance  of  a  small  engine  will  give,  accord- 
ing to  the  experimental  results  in  the  last  table,  '  =  96.8 

ol 

H.  P. ;  about  59  per  cent,  of  the  theoretical  rate  of  work  in  a 
perfect  engine,  or  of  the  rate  of  work  performed  by  a  boiler  in 
forcing  steam  through  an  orifice,  without  friction,  into  the 
atmosphere. 

In  regard  to  the  use  of  the  term  horse-power ',  it  must  be 
admitted,  however,  that  it  is  a  convenient  mode  of  designating 
the  capacity  of  land  boilers,  where  average  conditions  of  pres- 
sure and  rate  of  evaporation  are  understood. 

There  is,  however,  a  want  of  uniformity  among  manufac- 
turers in  regard  to  what  amount  of  heating-surface  shall  con- 
stitute a  horse-power,  with  chimney-drafts ;  the  amounts  vary- 
ing from  12  to  18  square  feet. 

249.  Kind  and  Quality  of  Materials. — The  materials  em- 
ployed in  the  construction  of  boilers  consist  of  plates,  rolled  or 
shaped  into  the  forms  necessary  for  the  shell,  tube-sheets  and  flues ; 
tubes,  or  flues,  formed  by  drawing,  or  by  lap- welding ;  rivets 
for  the  joints ;  rods  acting  as  stays  ;  plates,  or  castings,  for  the 
fronts  and  doors,  and  bars  for  the  grates.  Where  boilers  are 
set  in  brick- work  it  is  to  be  understood  that  the  external  work 
is  to  be  of  a  character  such  as  will  resist  the  action  of  heat  as 
well  as  prevent  its  dissipation  through  radiation  and  conduc- 
tion. 

The  materials  now  universally  used  for  the  shell  are  wrought 
iron  and  steel.  Cast  iron  is  sometimes  employed  for  the  heads 
of  small  cylinder  boilers,  and  for  steam-domes  or  steam- cham- 
bers, but  owing  to  its  rapid  deterioration  under  the  action  of  heat 
it  is  not  a  suitable  material  for  heating-surfaces.  It  is,  how- 
ever, employed  largely  in  the  fronts,  grate-bars,  for  attachments 
for  valves  and  pipes,  and  for  man-hole  and  hand-hole  plates. 

Copper  was  formerly  used  for  the  shells  of  marine  boilers  to 


176          THE  CONSTRUCTION  OF  STEAM  GENERATORS. 

some  extent  before  a  full  knowledge  was  acquired  of  the  favor- 
able properties  of  wrought-iron  plates  for  being  worked  into 
angular  shapes  by  bending  and  hammering  (technically  called 
"flanging  ").  This  material  is  now  confined,  however,  in  use,  to 
the  fire-boxes  of  locomotives,  and  in  some  cases,  as  in  fire-en- 
gine boilers,  to  small  tubes. 

Iron  boiler-plates  are  found  in  the  market,  in  this  country, 
under  three  general  designations,  which  indicate  to  some  extent 
not  only  the  qualities  of  the  plates,  but  also  the  modes  or  pro- 
cesses of  manufacture. 

Plate-iron  called  C.  No.  1  (charcoal  "No.  1 ;  or  iron  manufac- 
tured by  employing  charcoal  as  fuel  in  the  blast-furnace),  should 
be  used  only  in  parts  of  boilers  which  are  not  subjected  to  high 
degrees  of  heat.  Although  the  best  varieties  possess  sufficient 
strength  for  the  shells  of  boilers,  it  is  unsafe  to  use  this  quality 
of  iron  in  the  furnaces. 

Iron  called  C.  H.  No.  1  (charcoal-hammered  No.  1),  and  also 
"  flange  iron,"  comprises  plates  in  which  the  "  piles  "  are  re- 
heated and  hammered  with  heavy  steam-hammers.  This  pro- 
cess gives  greater  compactness  and  solidity  to  the  plate,  arid 
improves  not  only  its  strength,  but  also  its  capacity  for  resisting 
high  degrees  of  heat. 

Fire-box  iron  designates  a  kind  of  plate-iron  made  exclusive- 
ly for  furnaces. 

Of  each  of  these  kinds  there  are  many  different  qualities, 
depending  on  the  details  of  the  processes  in  the  different  facto- 
ries, and  the  care  with  which  the  iron  is  selected  and  the  plates 
fabricated.  In  this  branch  of  manufacture,  as  in  others,  the 
standing  and  reputation  of  particular  manufacturers  is  derived 
from  long-continued  and  satisfactory  use  of  their  products,  and 
is  a  sort  of  guarantee  of  quality. 

For  manufacturing  C.  No.  1  boiler-plate  the  iron  used  is 
generally  cold-blast  charcoal-iron.  The  pig-metal  is  remelted 
and  refined,  or  converted  into  wrought  iron,  in  charcoal  fires, 
the  balls  being  hammered  into  blooms.  These  blooms  are  re- 
heated in  reverberatory  furnaces,  and  then  rolled  into  slabs  about 
one  inch  thick.  These  pieces  are  called  covers.  Between  two 
covers  clippings  of  boiler-plates  are  compactly  placed,  and  the 
"  pile  "  is  then  reheated  to  a  welding  heat,  and  passed  between 
heavy  rolls.  Common  wrought  scrap  is  sometimes  piled  between 
the  covers,  and  of  course  the  risk  of  obtaining  inferior  iron  is 


THE  CONSTRUCTION  OF  STEAM  GENERATORS.          177 

thus  increased,  owing  to  imperfect  welding  of  the  pieces,  from 
the  occurrence  of  slag  between  the  layers. 

Iron  manufactured  by  this  process  of  covers  and  filling  is 
liable  to  blister  under  intense  heat,  on  account  of  its  laminated 
character,  and  from  imperfect  welding. 

The  charcoal-hammered  iron  is  that  which  is  produced  by 
piling  one  slab  or  bloom  upon  another,  no  scrap  being  intro- 
duced between  the  blooms,  or  by  piling  compactly  bars  at  right 
angles  to  each  other ;  the  piles  being  then  rolled  under  a  high 
welding  heat  to  compact  the  mass,  and  generally  reheated  and 
hammered  or  rolled  several  times.  The  quality  known  as  C.  H. 
No.  1  should  not  be  formed  of  covers  and  scrap,  whether  the 
piles  be  hammered  or  rolled ;  but  should  be  made  of  a  com- 
pact mass  of  homogeneous  material  solidly  welded  under  high 
welding  heats.  This  process  is  employed  to  produce  fire-box 
iron  also,  which  differs  from  the  C.  H.  No.  1  generally  in  being 
subjected  to  one  or  two  additional  processes  of  heating  and 
hammering  or  rolling;  and  in  which  the  greatest  care  is 
observed  in  the  selection  of  the  material. 

It  is  easy  to  see  how  much  depends  in  the  quality  of  iron 
boiler-plates  on  the  manufacturer,  and  that  there  may  be  as 
great  differences  in  quality  in  this  article  of  commerce  as  in 
fabrics  of  cotton  or  wool.  It  is  difficult  to  detect  on  a  super- 
ficial examination  differences  in  quality,  as  the  surfaces  of  dif- 
ferent qualities  appear  the  same.  As  a  general  rule,  plate -iron 
which  can  be  bent  to  right  angles  when  heated  to  a  red-heat 
without  showing  cracks  may  be  relied  on  for  all  parts  of 
boilers ;  and  the  indications  are  still  more  favorable  if  such  a 
test  can  be  successfully  made  when  the  plate  is  cold.  None 
but  the  very  finest  qualities  will  bear  this  latter  test. 

The  superiority  of  steel  plates  is  exhibited  under  these  tests. 

Where  a  test  by  actual  bending  or  working  is  impracticable, 
the  hammer  test  may  be  applied.  Each  plate  is  "  sounded " 
with  a  light  hammer  by  slightly  tapping  it  at  as  many  points  as 
possible.  Defects  arising  from  imperfect  welding  or  internal 
flaws  will  often  be  thus  discovered.  The  best  test  for  the  ten- 
sile strength  is  the  testing-machine  ;  and  where  a  large  number 
of  iron  plates  of  one  kind  is  to  be  used,  it  may  be  advisable  to 
send  samples  to  a  testing-macliine. 

Steel  plates  are  usually  made  from  puddled  or  c$st  steel. 
The  process  of  making  puddled  steel  is  to  stop  the  ordinary 
12 


178          THE  CONSTRUCTION  OF  STEAM  GENERATORS. 

puddling  process,  by  which  wrought  iron  is  made  from  pig 
iron,  at  the  moment  when  the  decarbonization  is  at  the  point 
required  for  steel. 

Homogeneous  steel  is  a  cast  steel  produced  by  melting 
wrought  iron  of  the  finest  quality  in  crucibles  with  carbona- 
ceous matter :  the  ingots  cast  are  heated  and  rolled  into  plates. 

It  is  apparent  that  these  steel  plates  must  produce  plates  of 
superior  quality,  not  only  on  account  of  their  great  strength, 
but  also  from  their  homogeneous  character. 

The  disadvantages  in  the  use  of  copper  arise  from  its  com- 
parative weakness,  especially  under  high  degrees  of  heat,  and 
its  cost.  For  fire-boxes  of  locomotives  it  is  almost  exclusively 
employed  in  England,  though  the  results  of  experience  in  this 
country  seem  to  be  in  favor  of  iron  for  this  purpose.  Steel 
plates  are  used  to  a  considerable  extent  for  locomotive  boilers, 
the  advantages  consisting  in  greater  strength  with  the  same 
weight,  or  equal  strength  with  less  weight;  while  this  material, 
from  its  homogeneous,  compact  structure,  resists,  better  than 
iron,  some  of  the  causes  of  deterioration,  such  as  corrosion  and 
attrition. 

250.  Stays  are  usually  made  of  the  finest  quality  of  wrought 
iron,  capable  of  bearing  a  tensile  strain  of  60,000  to  70,000  Ibs. 
per  square  inch.  Copper  stay-bolts  are  commonly  used  for  the 
fire-boxes  of  locomotives  in  England,  and  tubular  stays  are 
highly  recommended  by  some  engineers. 

The  material  employed  for  rivets  is  usually  wrought  iron,  the 
material  being  selected  and  the  rivet-rods  manufactured  for  this 
special  purpose,  so  as  to  combine  softness  under  the  hammer 
with  great  strength. 

Angle-iron  is  employed  by  English  manufacturers  for  con- 
necting the  heads  of  boilers  with  the  shells,  and  for  uniting 
the  ends  of  large  flues  to  the  heads ;  though  its  use  for  that 
purpose  has  not  extended  to  this  country.  This  is  in  part 
owing  to  the  superiority  of  the  best  American  boiler-plates  for 
flanging. 

Grate-bars  are  usually  made  in  this  country  of  cast  iron.  In 
England  wrought-iron  bars  are  used  in  locomotive  boilers. 
The  rapid  deterioration  of  grate-bars  renders  their  frequent  re- 
newal necessary,  and  as  this  is  easily  and  readily  accomplished, 
the  choice  of  the  least  expensive  material  seems  to  be  desirable. 
For  boiler  fronts  and  doors,  man-hole  and  hand-hole  plates,  etc., 


THE  CONSTRUCTION  OF  STEAM  GENERATORS.          179 

a  combination  of  cast  and  wrought  iron  is  used.  See  Plates 
XXXY.,  XXXVL,  XXXYIL,  pages  186*  186f,  186$. 

251.  Strength  of  the  Materials  used  in  Boilers. — Mr.  C.  B. 
Richards,  engineer  of  the  Colt's  Arms  Co.,  has  recently  made 
tests  of  several  varieties  of  boiler-plates  with  the  very  accurate 
testing-machine  of  that  company. 

The  tables  and  explanations  are  here  introduced  without 
comment,  as  Mr.  Richards's  skill  and  accuracy  in  experimental 
investigations  of  this  kind  are  well  known.  The  tables  give  a 
good  idea  of  the  resistance  to  tensile  strains  of  the  ordinary 
market  varieties  of  boiler-plates. 

The  experiments  of  Robert  Napier  &  Sons,  on  the  strength 
of  steel  and  iron  boiler-plates,  showed  the  mean  resistance  to 
tension  of  English  wrought-iroii  plates  to  be  49,000  Ibs.  per 
square  inch ;  the  result  of  150  experiments.  The  result  of  80 
experiments  gave  an  average  of  85,000  Ibs.  for  steel  plates. 
The  greatest  difference  between  the  highest  and  lowest  strengths 
of  the  same  brand  of  iron  plates  was  about  20,000  Ibs.  per 
square  inch.  For  steel  the  greatest  difference  was  about  the 
same.  The  greatest  average  difference  of  strength  of  plates 
across  and  with  the  grain,  was  for  iron  7,000  Ibs.,  for  puddled 
steel  about  22,000  Ibs.,  and  for  "  homogeneous "  steel  790  Ibs. 
per  square  inch. 

Fairbairn  gives  the  average  resistance  of  boiler-plates  52,000 
Ibs.  per  square  inch. 


180 


THE  CONSTRUCTION  OF  STEAM  GENERATORS. 


TABLES 

OF   THE   RESULTS    OF   A   NUMBER    OF    EXPERIMENTS   MADE 
BY   C.    B.    RICHARDS,    ENGINEER, 

ON   THE 
TENSILE    STRENGTH    OF   BOILER-PLATES. 

(Principally  on  those  rolled  by  the  Bay  State  Iron  Company.) 

TABLE  I. 


CQ 

•S 

«       tfs- 

Resistance  to  Tensile  Strain 

88 

d--0 

§ 

8.3' 

"^  •  'E  '1 

per  Square  Inch  of  Original 

*C    fl" 

02  2 

S 

§•  § 

o  jc  ^ 

Cross-Section. 

J  — 

z-  ^ 

II 

KIND  OF   IRON. 

Sj 

.HI 

||  J 

tc 

4J    C 

• 

. 

• 

g  S3 

6 

CM  J3 

4 

C  ^ 

11 

S    i4  § 

If 

0202 

If 

! 

I 

•t-i 

Resistai 
Inch  of 
.  A 

1     (From  an  old  Boiler.) 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

In. 

Lbs. 

2 

Thorneycroft,  English  

Short 

L 

47245 

46410 

46827 

j 

{     0.87 

V45293 

<        x 

2 

Do. 

C 

44355 

43165 

43760 

C 

1     0.27 

3 

Pennsylvania  "Common" 

L 

54899  :  44581 

492271  j 

0.87 

[-48484 

-\        x 

3 

Do. 

C 

54031 

43436   47641 

j     0.16 

1 

Pennsylvania  "  C.  No.  1  ". 

L 

48660,  1  M/)eQ 

2 

Do. 

C 

55218    53395 

54306  f0*' 

1 

Pennsylvania  "Flange"  .. 

L 

54466   |  Ko«oo 

2 

Do. 

C 

54819    51184    53001   f~luu 

OQT 

4 

Bay  State  "  C.  No.  1".... 

L 

58450    519<)2    54264   J  KonQ,{ 

.O( 

4 

Do. 

C 

53145    50449    51928  f5d< 

Ooo 

2 

Bay  State  "  Flange  "  

L 

57934    54377    56165   |  K/IQOK 

,**o 

2 

Do.                 ...   . 

C 

53998    53395 

53696'  f 

2 

Sligo  "  Fire-Box  "  ... 

53791  I  52546 

53168   >  Koven 

2 

Do. 

c 

54394    K0272 

52333  !  i 

(Specimen  from  a  different 

) 

source.)  • 

(    1.265 

1 

Do. 

M 

L 

60911 

1        x 

|    0.329 

TABLE  II. 


14 

Bay  State  "  Flange  "... 

Long 

L 

51378 

44036 

480981  ) 

63596 

12 

Do. 

C 

49023 

39898 

46277  ( 

1.25 

52349 

4 
4 

Bay  State  "C.  No.  1".... 
Do. 

u 

L 
C 

48819 
45240 

46086 
42961 

47725 
44301 

j-  46013 

'  0.80 

55967 
48849 

Bay  State. 

4 

Homogeneous  Metal  

M 

71139 

70100 

70672 

136473 

TABLE  III. 


1 

9 

Bay  State  "  Flange  "  
Do.       

Long 

L 
C 

47785 
49113 

46484 
46815 

47017 
47884 

[•  47450 

1.25x0.29 
0.75x0.29 

64411 
56755 

6 

Do.       

Short 

L 

5-2993 

50770 

51943 

i 

1.25x0.29 

(51296 

8 

Do.       

C 

53161 

51597 

52262 

0.75x0.29 

58170 

THE  CONSTRUCTION  OF  STEAM  GENERATORS. 


181 


"  The  results  given  in  these  tables  are  from  experiments  with 
specimens  of  three  different  shapes,  as  below :  " 


S' 


"  In  all  the  experiments  recorded  in  Table  I.  the  specimens 
were  shaped  like  either  S  or  S',  but  as  there  was  hardly  an  ap- 
preciable difference  in  the  results  from  these  two  forms,  they 
are  not.  separated  in  the  tables,  and  are  styled  c  Short  '  speci- 
mens." 

"  All  the  specimens  from  which  Table  II.  is  made  up  were 
shaped  like  L,  and  are  called  '  Long.' 

"  The  experiments  of  which  Table  TIL  gives  a  synopsis  were 
made  for  the  purpose  of  determining  the  influence  of  the  shape 
of  the  specimen  on  the  results  obtained  for  the  particular  mate- 
rial then  under  test.  All  these  specimens  were  taken  from  the 
same  piece  of  boiler-plate,  and  the  alternate  pieces  were  cut 
into  the  form  S  and  L  respectively." 

"  The  breaking-strain  per  square  inch  of  the  area  at  the  point 
of  fracture^  measured  after  fracture,  is  given  in  Tables  II.  and 
III.  That  this  value  gives  important  information  of  certain 
qualities  of  the  material  in  question,  is  indicated  by  the  fact 
that  it  shows  the  difference  between  the  toughness  or  ductility 
of  the  material  when  taken  crosswise  and  lengthwise  of  the 
plate,  better  than  the  other  values  of  breaking-strain  do.  The 
correctness  of  Kirkaldy's  opinion  on  this  point,  founded  on 
his  experiments,  has  thus  received  additional  confirmation." 

"  The  want  of  agreement  between  the  results  given  in  Tables 
I.  and  II.  for  Bay  State  plate,  is  to  be  accounted  for  entirely 
by  the  difference  in  shape  of  the  specimens;  as  shown  by 
Table  III." 


<>&  I 


182          THE  CONSTRUCTION  OF  STEAM  GENERATORS. 

The  tensile  resistance  of  copper  plates  is  about  36,000  Ibs. 
per  square  inch. 

The  influence  of  heat  upon  wrought  iron  is  to  increase  its 
tensile  strength  until  a  red-heat  is  approached^  when  its  strength 
rapidly  decreases.  For  copper,  the  decrease  of  strength  com- 
mences at  ordinary  temperatures,  and  at  about  1000°  F.  it  loses 
its  tenacity  in  a  great  degree. 

252.  Theory  of  Stress  in  Boilers. — By  the  term  "  stress  "  in 
applied  mechanics  is  meant  the  force  which  acts  directly  upon 
the  particles  of  any  material  to  separate  them. 

In  boiler  construction  the  adoption  of  the  cylindrical  form 
for  the  shell  and  flues,  or  tubes,  causes  this  stress  to  be  always 
a  tensile  stress  on  the  shell,  on  flues  subjected  to  internal  pres- 
sure, and  on  the  stays.  The  stress  is  a  compressive  one  on  flues 
or  tubes  subjected  to  external  pressure,  and  a  shearing  stress 
on  rivets.  Bending  moments  are  carefully  avoided  in  all  parts 
of  the  structure. 

The  tensile  stress  upon  the  material  of  a  cylindrical  shell 
tending  to  rupture  it  longitudinally  is  found  as  follows :  Let 
p  denote  the  elastic  force  of  the  steam  in  pounds  per  square 
inch,  d  the  diameter  of  the  cylinder,  t  the  thickness  of  the 
shell.  If  we  consider  unity  of  length  of  the  cylinder,  the  total 
force  tending  to  produce  rupture  will  be  p  d,  d  being  expressed 
in  inches.  The  total  resistance  of  the  material  will  be  2 1  x  f , 
f  being  the  resistance  to  tension  of  the  material ;  and  the  con- 
ditions of  equilibrium  require  that 

p  d  =  2  t  f , 
from  which  the  thickness  of  the  shell  is  obtained — 

_pd 
t~2f 

For  the  same  internal  pressure  and  the  same  material,  the 
thickness  for  different  diameters  will  be  proportional  to  the 
diameter.  For  the  stress  in  the  direction  of  the  axis  of  the 
cylinder,  the  total  pressure  in  this  direction  will  be  p  x  J  TT  da, 
and  the  resistance  of  the  material  in  the  cross-section  will  be 
f  X  TT  d  t.  Placing  these  quantities  equal  to  each  other,  we  have — 

pxJ-Trd3  —  f?rdt; 
or,  p  i  d  =  f  t 

d 


THE  CONSTRUCTION  OF  STEAM  GENERATORS.          183 

Tins  result  shows  that  the  area  of  resistance  to  rupture  in  the 
direction  of  the  axis,  relatively  to  the  total  area  of  pressure,  is 
double  that  in  the  first  case ;  or,  in  other  words,  the  stress  per 
square  inch  of  material  in  the  direction  of  the  axis  is  only  half 
that  which  tends  to  rupture  the  boiler  along  a  longitudinal 
plane  through  the  axis.  The  tenacity  f  may  be  taken  for  the 
bursting  tension,  the  proof  tension,  or  the  working  tension. 
Mr.  Fairbairn  gives  the  values  of  f  for  wrought  iron :  bursting 
tension,  34,000,  proof  tension,  17,000,  working  tension,  4,250 
Ibs.  per  square  inch.  This  is  equivalent  to  making  the  factor 
of  safety  8,  which,  however,  is  greater  than  that  usually  adopted 
in  practice.  It  is  assumed  that  the  working  pressure,  multi- 
plied by  the  factor  of  safety,  will  produce  rupture.  If  the 
working  pressure  be  60  Ibs.  per  square  inch,  for  example,  a 
pressure  of  480  Ibs.  per  square  inch  will  produce  rupture. 
Ordinary  boilers  constructed  for  a  working  pressure  of  60 
Ibs.  will  hardly  bear,  before  rupture,  480  Ibs.  Proof -tests 
of  double  the  working  pressure  are  allowed,  although  these 
tests  are  generally  limited  to  one  and  a  half  times  the  work- 
ing pressure.  Rankine  states  that  the  rule  followed  in  Eng- 
land is  to  make  the  working  pressure  one-sixth  of  the  bursting 
pressure. 

253.  Joints. — In  the  construction  of  boilers  the  junction  of  the 
plates  requires  special  care  and  attention,  inasmuch  as  the  re- 
sistance of  the  joints  determines  the  total  resistance.  Riveted 
joints  are  made  in  several  different  modes,  the  principal  of 
which  are  the  lap-joint  single-riveted,  the  lap-joint  double- 
riveted,  the  butt-joint  single-riveted,  and  the  butt-joint  double- 
riveted.  The  stress  upon  the  rivets  is  a  shearing  stress.  The 
butt-joint  is  formed  by  adjusting  the  edges  of  two  plates  and 
covering  the  joint  on  both  sides  by  covering-plates,  riveted 
either  with  one  or  two  rows  of  rivets  on  each  side  of  the  joint. 

The  construction  of  joints  by  these  various  methods  is  made 
on  the  following  principles  : 

Let  f  denote  the  resistance  per  square  inch  of  the  material 
of  the  plate  to  tearing,  f  the  resistance  of  the  rivets  per 
square  inch  to  shearing,  s  the  sectional  area  of  the  plate  which 
must  be  torn  apart,  s'  the  sectional  area  of  rivets  which  must 
be  sheared  to  produce  rupture.  Then  there  should  exist  the 

s'        f 

proportion  f  s  =  f '  s'  or  —  =  ^ .     For  wrought  iron  the  resist- 

s        i 


184:          THE  CONSTRUCTION  OF  STEAM  GENERATORS. 

ances  to  tearing  and  shearing  are  nearly  the  same,  and  -^  =  1, 

and  therefore  s'  should  be  equal  to  s.  If  t  be  the  thickness  of 
the  plate,  d  the  diameter  of  the  rivets,  c  the  distance  from 
centre  to  centre  of  rivets,  we  should  have  for  lap-joint  single 

*s' 
riveted,   —  —  1  —  sectional  area  of  one  rivet  ^  divided  by  sec- 

tional area  of  plate  between  two  rivet-holes. 


t(c-d) 
from  which 

0,7854  d2 
c  =  -  -  ---  f-  d 

L 

d  in  practice  is  usually  from  2t  to  1^^,  and  the  overlap  from 
c  to  1TV  c. 

For  overlapped  double-riveted  joints,  by  the  same  process 
the  value  of  c  may  be  found  to  be 


*  t 

the  overlap  in  practice  being  from  If  c  to  If  c. 

For  butt-joints  with  a  pair  of  covering-plates,  single-riveted, 
the  value  of  c  is  the  same  as  for  overlapped  double-riveted 
joints  ;  the  length  of  each  covering-plate  2,  the  overlap  =  2  c 
to  2^  c.  For  double-riveted  butt-joints 

3.1416    , 
c  =  —  __  +  d 

t 

the  length  of  each  covering-plate  being  3-J  to  3£  c. 

The  order  of  strength  of  these  joints,  in  terms  of  the 
strength  of  the  original  plate,  according  to  Clark,  are  for  plates 
f-inch  thick  and  less, 

Working  Strength. 

t  Original  strength  of  plate  .  .  .   100         11,000  Ibs.  per  sq.  inch. 
Single-riveted  lap-joint  .......     60  6,700         "         " 

Double-riveted  lap-joint  .......     72  8,000         "         " 

Double-riveted  butt-joint  ......      80  9,000         "         " 

The  above  figures  are  given  for  the  best  English  Yorkshire 
plates. 

*  Rankine.  .  \  Holley. 


THE  CONSTRUCTION  OF  STEAM  GENERATORS.          185 

Fairbairn  estimates  the  strength  of  joints  to  be,  in.  terms  of 
the  strength  of  the  plate, 

Strength  of  plate 100         Bursting  tension .   34,000  Ibs. 

Double-riveted  joint 70         Proof  tension 17,000   " 

Single-riveted  joint 56         Working  tension.     4,250   " 

the  working  tension  being  •§•  of  the  bursting  tension.  For 
cast-iron  pipes  the  working  tension  may  be  estimated  at  -J-  the 
bursting  tension,  and  the  values  of  the  tenacity  in  practice 
may  be  estimated  at 

16,500  Ibs.  per  sq.  inch  for  bursting  tension. 
5,500   "       "         "         "     proof  tension. 
2,750   "       "         "         "     working -tension. 

Welded  joints  for  boilers  have  been  found  to  possess  the 
same  strength  as  the  original  plate,  but  practical  difficulties 
prevent  the  adoption  of  this  process  for  ordinary  work. 

The  thickness  of  boiler-plates  is  practically  limited  in  both 
directions.  Very  thin  plates  cannot  be  caulked,  and  very  thick 
plates  cannot  be  riveted.  The  limits  are  practically  about  i  of 
an  inch  for  the  lower  limit  and  f  of  an  inch  for  the  higher  limit. 
The  riveting  machine  is  essential  for  very  thick  plates,  a  thick- 
ness of  half  an  inch  being  near  the  limit  of  hand-riveting.  The 
usual  thicknesses  for  boilers  are  J,  -3^-,  f ,  -j^,  -J. 

254.  Resistance  of  Flues  to  Collapse. — The  resistance  of  flues 
to  collapse  from  external  fluid  pressure  was  found  experiment- 
ally by  Fairbairn  to  be  inversely  as  the  length,  inversely  as  the 
diameter,  and  directly  as  a  power  of  the  thickness,  which  for 
practical  purposes  may  be  represented  by  2 ;  and  the  following 
formula  is  given  by  Rankine  for  the  collapsing  pressure  of  an 
iron  flue.  Let  p  be  the  collapsing  pressure  in  pounds  per 
square  inch,  t  the  thickness  expressed  in  inches,  d  the  diameter, 
also  expressed  in  inches,  and  1  the  length  expressed  in  feet. 
Then— 

p  =  806,000  P 

This  formula  is  only  applicable,  however,  for  flues  of  ordi- 
nary lengths,  such  as  those  in  use  in  steam-boilers.  When  flues 
are  strengthened  by  angle-iron  rings  riveted  around  them  the 
length  1  is  to  be  taken  between  the  rings.  The  plates  from 
which  large  flues  are  formed  are  usually  of  the  same  thickness 


186          THE  CONSTRUCTION  OF  STEAM  GENERATORS. 

with  those  of  the  shell.  The  resistance  to  collapsing  between 
two  rings  should  be  equal  to  the  resistance  of  the  shell  to  the 
bursting  pressure. 

255.  Stays. — Wherever  flat  surfaces  occur,  which  are  exposed 
to  pressure,  it  becomes  necessary  to  introduce  stays  or  bolts  to  re- 
sist the  pressure — the  stays  being  connections  between  plates 
in  the  form  of  tie-bars,  which  resist  the  separation  of  the  plates. 
Fig.  4,  page  137,  exhibits  the  mode  of  introducing  stays  for 
marine  boilers,  and  Plate  XXIV.,  page  138,  the  general  method 
for  locomotive  boilers.  Each  stay  sustains  the  pressure  of  the 
steam  against  a  certain  area  of  the  plate  to  which  it  is  attached, 
and  the  sectional  area  of  the  stay,  multiplied  by  the  resistance 
of  the  material  per  square  inch,  should  be  equal  to  the  product 
of  the  area  which  is  to  be  sustained,  multiplied  by  the  pressure 
of  the  steam  per  square  inch.  The  factor  of  safety  for  stays 
is  8.  The  usual  distance  apart  of  the  stays  of  locomotive  boil- 
ers is  4^-  to  5  inches,  and  of  low-pressure  marine  boilers  10  to 
12  inches.  Where  the  stays  are  likely  to  become  corroded  the 
working  tension  should  not  be  greater  than  3,000  to  4,000  Ibs. 
per  square  inch,  or,  in  other  words,  a  larger  factor  of  safety 
should  be  employed.  The  crowns  of  locomotive  furnaces  are 
usually  hung  by  stays  or  bolts  from  a  system  of  ribs  or  beams 
which  cross  it  in  parallel  lines,  the  ends  being  supported  on  the 
front  and  back  vertical  ends  of  the  fire-box,  the  beams  being 
also  hung  from  the  roof  or  shell.  The  crown-sheets  of  the 
locomotive  fire-boxes  being  usually  flat,  and  being  exposed  to 
intense  heat,  the  utmost  care  is  necessary  in  this  part  of  the 
construction.  The  pressure  of  1  pound  per  square  inch  of 
steam,  upon  one  square  foot  of  surface,  being  equivalent  to  about 
the  weight  of  one  cubic  foot  of  ordinary  sandstone,  and  100 
pounds  per  square  inch,  consequently,  will  give  a  pressure  equiv- 
alent, approximately,  to  the  weight  of  a  column  of  sandstone 
100  feet  high.  The  weight  to  be  borne  by  the  flat  crown  of  a 
fire-box  3x4  sustaining  a  pressure  of  100  pounds  per  square 
inch  would  thus  be  approximately  equivalent  to  the  weight  of 
a  column  of  sandstone  having  a  base  of  12  square  feet  and  an 
altitude  of  100  feet.  It  is  this  weight  that  must  be  resisted  by 
the  stays  and  their  attachments. 

The  construction  of  cast-iron  boiler  fronts,  for  the  setting  of 
boilers  in  brick-work,  is  shown  in  Plate  XXXV.,  page  186*. 
Plate  XXXVI.,  page  186f,  shows  the  ordinary  construction  of 


THE  CONSTRUCTION  OF  STEAM  GENERATORS.        186* 


THE  CONSTRUCTION  OF  STEAM  GENERATORS.  186f 


THE  CONSTRUCTION  OF  STEAM  GENERATORS.          187 

furnace  doors  for  marine  boilers,  and  Fig.  6,  page  137,  the 
usual  method  of  setting  grate-bars  in  marine  boilers. 

256.  Supply  of  Feed-water.  —  The  supply  of  water  to  a  boiler 
is  of  course  indispensable  to  its  performance.  It  is  usually  ac- 
complished by  an  independent  apparatus,  a  pump  or  an  injec- 
tor being  employed. 

The  capacity  of  the  feeding  apparatus  should  be  such  as  to 
supply  sufficient  water  not  only  for  the  highest  rate  of  evapora- 
tion likely  to  be  attained,  but  to  supply  all  losses  from  prim- 
ing, leakage,  blowing  off,  etc. 

Care  should  be  taken  that  the  feed-water  does  not  impinge 
on  the  plates  or  flues,  as  the  sudden  cooling  at  one  point  is 
liable  to  fracture  the  plates.  Such  fractures  cannot  always  be 
discovered  when  the  boilers  are  inspected,  and  are  always  a 
source  of  danger. 

For  land  engines  a  capacity  of  two  and  a  half  times  the 
net  feed  -water  required  by  the  engine  is  the  rule  given  by 
Rankine. 

Proper  arrangements  for  regulating  the  supply  to  the  boiler 
are  required.  Where  steam  is  used  for  heating  purposes  the 
condensed  steam  is  returned  to  the  boiler  by  the  action  of 
gravity,  the  waste  being  supplied  from  time  to  time  by  the  at- 
tendant, through  a  cock  operated  by  hand. 

Feed-water  Heaters  are  devices  by  which  the  exhaust-steam 
from  engines  is  caused  to  pass  through  pipes,  through  which 
the  feed-water  also  flows  in  contact  with  these  pipes.  A  part 
of  the  waste  heat  of  the  engine  is  thus  utilized  in  raising  the 
temperature  of  the  feed-water  before  it  reaches  the  boiler. 
The  saving  effected,  in  units  of  heat,  is  the  quantity  of.  heat, 
nearly,  required  to  raise  the  temperature  of  the  feed-water 
from  its  natural  temperature  to  the  temperature  at  which  it  is 
supplied  to  the  boiler. 

x  - 


01 


CHAPTER  VII. 

BOILER   EXPLOSIONS. 

257.  THE  risk  of  life  and  property  which  attends  the  use  of 
the  steam-boiler  has  always  been  a  source  of  constant  anxiety 
to  the  engineer  and  to  the  public.  Explosions  continually  take 
place  under  circumstances  of  the  utmost  apparent  security : 
as  they  occur  without  warning  and  occupy  but  an  instant  of 
time,  it  is  generally  impossible,  except  in  rare  instances,  to 
ascertain  with  certainty  their  true  cause,  and  there  is  seldom  a 
unanimous  opinion  on  the  part  of  experts  who  examine  into 
the  causes  after  the  event.  The  loss  of  life  and  damage  to 
property  often  produce  great  public  excitement  and  private 
distress,  and  are  sometimes  followed  by  suits  for  damages  or  in- 
dictments for  manslaughter.  The  question  of  possible  or  pro- 
bable causes  has  thus,  to  some  extent,  assumed  a  judicial  aspect, 
and  it  becomes  a  matter  of  serious  importance  not  only  to  as- 
certain how  far  explosions  may  be  prevented,  but  also  the  de- 
gree of  individual  responsibility  to  be  attached  to  them. 

It  has  been  remarked  that  the  conditions  of  safety  and 
economy  in  the  case  of  steam  generators,  as  in  nearly  all  other 
structures,  are  in  direct  antagonism — economy  of  construction 
demanding  the  least  amount  of  costly  materials,  and  safety  re- 
quiring such  an  excess  of  strength  as  shall  place  accidents  be- 
yond all  contingencies  of  use  and  management.  In  the  forms 
of  boilers  which  are  most  exposed  to  explosions,  it  is  customary 
to  provide  theoretically  for  a  factor  of  safety  of  six  to  eight ; 
that  is,  an  internal  pressure  of  six  or  eight  times  the  working 
pressure  is  supposed  to  be  sufficient  to  produce  rupture. 

This  theoretical  factor  is,  however,  seldom  realized.  It  is 
doubtful  whether  boilers  of  the  common  forms  are  ever  manu- 
factured so  strong  that  four  times  the  working  pressure,  if 
applied,  would  not  cause  permanent  injury  or  rupture,  and  proof- 
tests  of  three  times  the  working  pressure  would  be  objected  to 
by  any  manufacturer  on  the  ground  that  it  would  permanently 
injure  the  structure. 

The  subject  is  here  introduced  and  discussed  in  some  of  its 


BOILER  EXPLOSIONS.  189 

aspects,  not  for  the  purpose  of  presenting  any  special  theories 
or  views,  but  to  illustrate  some  of  the  applications  of  the  funda- 
mental principles  of  the  dynamic  theory  of  heat  to  this  question. 
There  are  evidently  numerous  possible  causes  of  explosion,  some 
of  which  may  be  subjected  to  exact  analysis — and  means  of 
preventing  such  causes  may  be  provided  ;  while  there  are  sup- 
posed to  be  other  causes  not  yet  fully  understood.  In  a  great 
majority  of  cases  it  is  safe  to  say,  however,  that  explosions  arise 
from  defects,  or  other  causes,  simple  enough  in  themselves,  but 
which,  at  the  moment,  are  either  hidden  from  observation  or 
are  unavoidable  accidents.  Excellence  in  materials  and  work- 
manship, and  intelligence  and  watchfulness  on  the  part  of  the 
attendant,  are  the  surest  guarantees  of  safety.  "Where  such 
narrow  limits  exist,  although  it  may  not  be  possible  to  state 
positively  all  the  causes  of  explosions,  yet  some  of  the  more 
evident  sources  of  danger  may  be  pointed  out. 

It  may 'be  asserted,  for  instance,  as  a  self-evident  truth,  that 
the  real  or  remote  causes  of  all  explosions  may  be  reduced  to 
two  proximate  causes.  First,  insufficient  strength  of  the 
structure  to  resist  the  ordinary  working  pressure.  Such  a  de- 
ficiency in  strength  may  arise  from  an  original  defect  in  the 
materials  or  workmanship,  at  the  time  of  construction,  or  it 
may  be  due  to  deterioration  from  use,  from  ordinary  wear  and 
tear,  or  from  injuries  occurring  from  mismanagement,  wrant  of 
attention,  and  repairs,  etc.  Manufacturers  and  engineers  are 
supposed  to  comprehend  fully  these  causes  of  danger,  and  it  is 
the  object  of  good  engineering  and  good  management  to  avoid 
them. 

The  second  cause  of  danger  arises  from  an  accumulation  of 
pressure  within  the  boiler,  to  a  dangerous  degree,  above  that 
which  the  structure  is  designed  to  resist.  When,  the  limits  of 
safe  "working  pressure  are  exceeded,  the  danger  begins ;  and 
beyond  a  safe  proof -tension  it  becomes  imminent. 

The  accumulation  of  pressure  may  be  gradual  and  due  sim- 
ply to  the  increase  which  accompanies  a  continued  evaporation 
when  there  is  not  sufficient  outlet  for  the  steam  constantly 
formed,  or  it  may,  according  to  prevailing  ideas,  arise  from  a 
sudden  evolution  of  steam  in  amounts  too  great  for  any  ordi- 
nary means  of  efflux  ;  extraordinary  stresses  being  brought  to 
bear  from  the  expansive  forces  thus  generated. 

First,  in  regard  to  gradually  increasing  pressure,  to  what 


190  BOILER  EXPLOSIONS. 

extent  may  the  engineer  or  stoker  be  held  responsible,  or  what 
degree  of  watchfulness  is  necessary  on  his  part  ? 

One  question  to  be  solved  is,  at  what  rate  in  time  will  the 
pressure  in  any  given  boiler  increase  if  there  is  a  constant  rate 
of  ordinary  evaporation,  and  no  outlet  for  the  steam  ?  and  an- 
other, to  what  extent  can  the  engineer  trust  the  ordinary  safety- 
valve  to  prevent  this  gradual  increase,  or  to  furnish  an  outlet 
for  the  steam  ? 

The  rate  of  increase  of  pressure  may  be  found  theoretically 
by  means  of  a  formula  given  by  Professor  Zeuner  in  his  work 
on  the  Mechanical  Theory  of  Heat. 

Let  T  be  the  time,  in  minutes,  which  must  elapse  from  the  in- 
stant that  all  efflux  of  steam  is  prevented  in  a  boiler,  to  the  in- 
stant when  a  dangerous  or  bursting  pressure  must  follow ; 

Let  w  represent  the  weight  of  water  in  the  boiler ; 

t,  the  temperature  of  the  water  due  to  a  dangerous  pres- 
sure; 

t  the  temperature  due  to  the  working  pressure ; 

Q  the  quantity  of  heat,  in  British  units,  transferred  to  the 
water  per  minute : 

Then, 

T  =  w  (t,  -  t) 

Q 

will  give,  with  a  sufficient  degree  of  approximation,  the  time  in 
minutes  ;  the  mean  specific  heat  of  water  being  taken  as  unity. 

This  formula  shows  that  the  time  will  be  proportional  di- 
rectly to  the  amount  of  water  in  the  boiler,  to  the  difference  of 
temperatures  ti  and  t,  and  inversely  proportional  to  the  quan- 
tity Q.  The  fluctuations  of  pressure  will  be  less  rapid  in  boilers 
which  contain  large  quantities  of  water,  and  have  at  the  same 
time  a  low  rate  of  evaporation.  Such  conditions  are  found  es- 
pecially in  marine  boilers  ;  while  the  reverse  is  true  for  boilers 
containing  small  quantities  of  water,  and  having  rapid  rates  of 
evaporation,  such  as  locomotive  and  fire-engine  boilers.  The 
fluctuations  will  also  evidently  be  more  rapid  at  high  pressures 
than  at  low  pressures,  since  at  high  pressures  a  greater  change 
of  pressure  occurs  with  an  equal  difference  of  temperatures, 
than  at  low  pressures. 

258.  The  following  examples,  as  illustrations,  will  exhibit 
the  applications  of  the  formula : 


BOILER  EXPLOSIONS.  191 

EXAMPLE  I. 

A  marine  tubular  boiler  of  the  largest  size,  such  as  that  ex- 
hibited page  136. 

w  =  79,000  Ibs.  of  water. 

Suppose  the  working  pressure  to  be  2^  atmospheres,  and  the 
dangerous  pressure  to  be  4  atmospheres. 

The  boiler  contains  5,000  square  feet  of  heating-surface;  and 
supposing  the  evaporation  to  be  3  Ibs.  of  water  per  hour  for 
each  square  foot  of  heating-surface,  we  shall  have,  taking  as  a 
sufficient  approximation  in  round  numbers,  1,000  units  of  heat 
as  the  thermal  equivalent  of  the  evaporation  of  1  Ib.  of  water. 

ti  _  t  =  29°  F. 
5000  x  3  x  1000 


79000  x  29  0,      . 

T  ~~=  5000  x  3  x  1000  ==  91  mmUteS 
60 


EXAMPLE  II. 

A  locomotive  boiler,  containing  5,000  Ibs.  of  water,  having 
11  square  feet  of  grate-surface,  and  burning  60  Ibs.  of  coal  per 
hour  on  each  square  foot  of  grate.  Each  pound  of  coal  will 
evaporate  about  7  Ibs.  of  water  per  hour,  making  77  Ibs.  of 
water  evaporated  per  minute. 

Suppose  the  working  pressure  to  be  90  Ibs.  per  square  inch 
and  the  dangerous  pressure  to  be  175  Ibs.  From  the  table 
page  53,  we  have  t,—  t  =  50°  F. 

5000  x  50 
T  =  7710000  =  3*  mmutes 

EXAMPLE  III. 

The  Steam  Fire-Engine. — Taking  an  actual  case.  The 
boiler  contains  338  Ibs.  of  water  and  has  157  square  feet  of 
heating-surface.  Supposing  each  square  foot  of  heating-sur- 
face to  generate  only  1  Ib.  of  steam  in  one  hour,  the  pressure 
will  rise  from  100  to  200  Ibs.  in 

T  =  7  minutes 


192  BOILER  EXPLOSIONS. 

EXAMPLE  IY. 

To  find,  in  the  same  boiler,  how  long  a  time  will  be  required 
to  get  ii/p  steam  •  that  is,  for  instance,  to  carry  the  pressure 
from  0  to  100  Ibs.     If  we  suppose  only  1^  cubic  feet  of  water 
to  be  introduced  into  the  boiler  at  first,  we  shall  have 
93    x  117 


1000 


=  41  nmmteB 


60 

The  formula  shows  that  if  w  is  diminished  by  any  cause,  the 
time  T  is  diminished  in  the  same  proportion.  The  lowering 
of  the  water  in  a  boiler  from  failure  of  the  feed-apparatus  in- 
creases the  danger  of  explosion,  therefore,  not  only  by  exposing 
plates  to  overheating,  but  by  causing  a  more  rapid-  rise  of 
pressure  for  the  same  rate  of  combustion  ;  while  it  is  not  im- 
probable that  the  rate  of  evaporation  is  increased  from  the 

same  cause,  and  a  further  diminution  of  -  thus  produced. 

These  examples,  deduced  from  purely  theoretical  considera- 
tions, have  been  confirmed  by  experiments,  and  serve  to  indi- 
cate the  degree  of  watchfulness  required  on  the  part  of  the 
engineer. 

259.  Safety-  Valves.  —  It  is  supposed  that  the  gradual  increase 
of  pressure  above  discussed  can  never  take  place  if  the  safety- 
valve  is  in  good  working  order,  and  if  it  have  proper  propor- 
tions. Upon  this  assumption,  universally  acquiesced  in,  at  least 
by  the  public,  when  there  is  no  other  accountable  cause,  explo- 
sions are  often  attributed  to  the  "  sticking  "  of  the  safety- 
valve,  "bent  valve-stems,"  or  "inoperative  valve-springs." 

As  the  safety-valve  is  the  sole  reliance  in  case  of  neglect  or 
inattention  of  the  engine-driver,  it  is  important  to  examine  its 
mode  of  working,  and  the  ordinary  methods  of  construction. 
It  should  be  observed,  however,  that  engineers  do  not,  in  prac- 
tice, place  their  trust  in  the  safety-valve  alone,  and  that  to 
their  watchfulness  and  attention  the  public  are  more  indebted 
for  safety  than  to  the  apparatus  which  is  designed  to  regulate 
the  pressure.  The  skill  with  which  a  good  engineer  will  regu- 
late the  pressure  by  checking  the  evaporation  (by  opening  the 
fire-doors,  or  the  connection-doors,  and  by  other  appliances),  is 
the  chief  source  of  safety  as  far  as  regards  a  gradual  increase 
of  pressure,  and  the  safety-valve  is  probably  oftener  opened 


BOILER  EXPLOSIONS.  193 

sufficiently  by  hand,  under  critical  circumstances,  than  by  the 
action  of  its  own  mechanism.  It  is,  however,  an  indispensable 
adjunct  to  a  steam  generator,  and  should  be  made,  if  possible, 
such  that  under  its  automatic  action  no  considerable  increase 
of  pressure  above  the  working  pressure  will  be  possible  from 
ordinary  evaporation. 

The  ordinary  safety-valve  is  a  disk  with  a  beveled  edge, 
resting  on  a  corresponding  seat.  The  disk  is  kept  down 
against  the  boiler-pressure  by  external  pressure  variously  ap- 
plied, either  by  a  weight  acting  with  a  leverage  or  by  a  spring. 
The  opening  for  the  efflux  of  steam,  created  by  the  rise  of  the 
valve,  is  thus  .an  annular  opening,  the  area  of  which  may  be 
approximately  found  by  multiplying  the  mean  circumference 
of  the  disk  by  the  rise  of  the  valve  measured  perpendicularly 
to  the  beveled  edge.  Representing  the  opening  by  o,  the 
height  of  rise  by  1,  and  the  mean  circumference  by  c,  the  open- 
ing or  orifice  will  be  approximately 

o  =  1   x  c 

The  quantity  c,  or  at  least  the  area  of  the  disk  of  which  c  is 
the  circumference,  is  variously  estimated  in  practice,  and  is  in 
most  countries  fixed  by  ordinances  ;  the  rules  established  being 
based  on  experiments.  One  English  rule  is  that  the  safety- 
valve  area  shall  have  half  a  square  inch  for  each  square  foot 
of  fire-grate,  or,  .025  of  a  square  inch  for  each  square  foot  of 
heating-surface.  Others,  quoted  by  Rankine,  are  as  follows  : 
Let  A  be  the  area  of  the  piston,  v  its  velocity  in  feet  per  min- 
ute, P  the  excess  of  pressure  in  the  boiler  above  that  of  the  at- 
mosphere in  Ibs.  on  the  square  inch,  then  the  area  will  be 


Another  quoted  by  the  same  author  is  :  "  a  =  area,  in  square 
inches  —  from  ^  to  -^  of  the  number  of  Ibs.  of  coal  burned 
per  hour,  or  a  the  area  in  square  inches  =  y^  to  y^  of  the 
water  evaporated  per  hour." 

The  French  rule  for  the  diameter  of  the  valve,  as  given  by 
Peclet,  is 


D  = 


-  0.412 

s 

n  -  0.412 
13 


or  s'  =  5.30 


194  BOILER  EXPLOSIONS. 

in  which  D  is  the  diameter  in  centimetres,  and  s'  the  area  in 
square  centimetres,  of  the  disk,  s  representing  the  heating-sur- 
face of  the  boiler  in  square  metres,  and  n  the  number  of  at- 
mospheres of  pressure. 

The  laws  of  Prussia  require  that  the  area  of  the  valve  shall 
be  determined  by  a  rule  which  may  be  practically  stated  as  fol- 
]ows :  P  being  the  absolute  internal  pressure,  the  area  of  the 
disk  in  square  inches  for  each  square  foot  of  heating-surface 

may  be  found  by  the  formula,  a  =  — '-—-^.      These  various  for- 

p  +  15 

mulas  give  the  area  of  the  disk,  or  pipe  closed  by  the  valve — 
not  the  orifice  o,  as  determined  by  the  equation  o  —  1  x  c. 

For  the  determination,  theoretically,  of  the  orifice  necessary 
for  the  efflux  into  the  atmosphere  of  any  given  quantity  of  steam 
under  any  given  pressure,  the  velocity  of  the  issuing  steam  must 
be  ascertained.  If  we  suppose  a  unit  of  weight  of  steam  to 
issue  from  an  orifice  with  a  velocity  v,  the  living  force  of  this 

v3 
mass  will  be  — — ,  and  this  expresses  a  quantity  of  work  which 

is  performed  by  unit  of  weight  of  the  steam  in  expanding  from 
the  pressure  and  volume  p2  v3  in  the  boiler  to  the  pressure 
pl  Vj  of  the  atmosphere  ;  for  this  is  the  work  wThich  actually 
produces  the  velocity  v.  This  work  for  expanding  steam,  or 
air,  when  the  heat  which  is  converted  into  work  is  drawn  from 
the  steam  or  air  itself,  can  be  found  when  the  curve  of  expansion 
is  known :  this  curve  is  called  the  adiabatic  curve,  a  term  applied 
by  Mr.  Rankine  to  curves  of  expansion  when  no  heat  is  imparted 
to  or  abstracted  from  the  expanding  gas  or  vapor.  The  equa- 
ls 
tion  of  such  a  curve  has  the  form  p  v  =  a  constant  quantity, 

and  this  equation,  first  introduced  by  Poisson,  is  that  from  which 
the  laws  of  the  pressures,  volumes,  and  temperatures  given  on 
page  33  are  obtained,  known  as  Poisson's  equations.  From  these 
equations  the  expression  for  the  work  of  1  unit  of  weight  of 

v2  k 

steam  will  be  - —  =  =- — -  (p2   v2  —  pj   v^,    from  which  the 

value  of  v  can  be  obtained. 

When  steam  or  air  issues  from  a  short  cylindrical  or  conoi- 
dal  opening  into  the  atmosphere,  the  orifice  of  the  cylinder  or 
cone  is  not  that  at  which  the  pressure  becomes  reduced  to  the 


BOILER  EXPLOSIONS.  "195 

atmospheric  pressure,  but  that  reduction  occurs  at  a  point  be- 
yond, where  the  escaping  steam  spreads  out  into  a  conical  shape  ; 
and  hence  the  area  of  section  in  which  the  pressure  pL  is  equal 
to  the  atmospheric  pressure  is  greater  than  the  actual  orifice, 
or  throat  of  the  stream.  Supposing  the  velocity  to  have  been 
found  by  the  equation  just  given,  the  quantity  of  steam  which 
flows  in  a  second  wdll  depend  on  tnis  effective  or  greater  section 
of  the  issuing  stream,  and  also  on  the  specific  volume  of  the  va- 
por in  this  section. 

Let  w  be  the  weight  issuing  in  a  second. 

Y,  the  velocity. 

F,  the  section  where  the  pressure  is  p , . 

v,  the  specific  volume  at  the  same  point. 

Then  evidently  w  =  -  -  x  F,  an  equation  from  which  the 

section  F  may  be  found. 

Professor  Zeuner  gives,  in  his  work  on  the  Mechanical  Theo- 
ry of  Heat,  the  values  of  Y  and  of  w  for  different  absolute 
pressures  in  the  boiler  (the  external  pressure  being  constant), 
from  2  to  14  atmospheres.  He  states  that  the  values  of  Y  thus 
determined  are  to  be  multiplied  by  a  coefficient,  which  depends 
partly  on  the  form  of  the  outlet,  and  partly  on  the  pressures  ; 
this  coefficient  to  be  determined  by  experiment.  Such  experi- 
ments were  subsequently  made  by  Mr.  R.  D.  Napier,  who  pro- 
posed an  empirical  formula  (given  in  the  Appendix  A).  The 
formula  of  Mr.  Rankine,  based  on  the  experiments  of  Napier, 
also  given  in  the  Appendix,  for  the  outflow  of  steam  (stated  by 
him  to  be  a  rough  practical  formula),  when  the  pressure  in  the 
boiler  is  equal  to  or  greater  than  j-  the  external  pressure,  is 

w  =  ^y,  that  is,  the  weight  of  steam  discharged  from  an  ori- 
fice of  unit  of  area  in  the  throat,  in  one  second,  is  one-seven- 
tieth of  the  pressure  on  the  same  area  in  the  boiler. 

By  this  rule  it  becomes  easy  to  find  the  orifice  necessary  for 
the  discharge  of  a  given  quantity  of  steam. 

The  number  of  pounds   discharged  per  square   inch   per 

second  being  w  =  2l_,  the  quantity  for  the  area  A  in  square 
inches  will  be  AW  =^XA="W 

70 w  LI  B  U  A  it  i 

A  ~  ""P" 

UNIVKUSITY   OF 

CALIFORNIA. 


196  BOILER  EXPLOSIONS. 

EXAMPLE. 

260.  Suppose  a  boiler  to  evaporate  1,800  Ibs.  of  water  per  hour, 
what  area  of  orifice  (supposed  to  have  the  form  of  a  cone  of 
the  shape  of  the  contracted  vein)  will  be  sufficient  for  the  dis- 
charge of  all  the  steam,  the  pressure  in  the  boiler  being  4  at- 
mospheres, or  58.8  Ibs.  per  square  inch  ;  we  shall  have  A  = 

70        1800        70 


58       3600       58          ' 

The  application  of  the  purely  theoretical  formula  of  Professor 
Zeuner,  referred  to,  would  give  for  the  orifice  under  these  con- 
ditions 0.782  square  inches.  His  ultimate  theoretical  formula, 
given  in  the  Appendix,  may  be  applied  by  taking  from  the  table 
there  given  the  proper  coefficient,  under  the  head  of  dry-steam, 
0.768,  giving  0.782  x  0.768  =  0.60,  the  same  as  above. 

This  method  of  finding  the  orifice  is  applicable  only  to  ori- 
fices of  the  particular  form  above  mentioned  ;  if  it  be  applied 
to  finding  the  necessary  orifice  for  safety-valves,  it  must  be  as- 
sumed that  the  conditions  for  an  annular  orifice,  such  as  that 
described  for  the  safety-valve,  are  the  same  as  for  the  conoidal 
nozzle. 

The  orifice  of  flow  in  such  a  case  being  approximately  found 
by  multiplying  the  rise  of  the  valve  by  the  circumference,  o  = 
1  x  c,  we  shall  have 

70 
lx    c  =  A  —  --  x  W,  for  all  cases  in  which  the  internal  pres- 

sure is  equaL  to  or  greater  than  |-  of  the  external  pressure. 

It  is  somewhat  doubtful  whether  this  assumption  in  regard  to 
the  orifice  for  common  safety-valves  can  be  permitted,  but  it 
must  be  approximately  correct  for  practical  purposes. 

The  quantity  1,  or  rise  of  the  valve,  being  determined  by  the 
resultant  of  the  forces  or  pressures  acting  on  the  upper  and  lower 
faces  of  the  disk,  has  not  been  theoretically  determined  ;  and  it 
is  doubtful  if  it  can  be  so  determined.  When  a  safety-valve,  as 
ordinarily  constructed,  rises  from  its  seat,  it  is  supposed  to  stand 
free  from  its  seat  all  around,  and  to  be  supported  simply  by  the 
pressure  of  the  outflowing  steam  ;  but  there  is  no  doubt  that 
in  all  cases  lateral  pressures  act  in  such  a  way  as  to  cause 
the  valve  to  press  on  one  side  or  the  other  against  its  seat,  thus 
giving  rise  to  a  small  amount  of  friction. 


BOILER  EXPLOSIONS.  197 

The  pressure  underneath  the  valve  after  steam  commences  to 
flow  is  always  less  than  the  boiler-pressure.  For  the  maximum 
flow,  which  occurs  for  a  given  orifice  when  the  internal  pressure 
is  about  f  of  the  external  pressure,  the  pressure  underneath  the 
valve  will  bear  approximately  this  ratio  to  the  boiler-pressure  ; 
and  to  maintain  a  valve  in  a  position  away  from  its  seat,  the 
boiler-pressure  must  always  rise  above  that  at  which  the  valve 
is  set.  This  increase  of  pressure  is  at  present  an  unknown 
quantity,  when  taken  in  connection  with  the  action  of  valves 
blowing  off  steam. 

The  quantity  1  or  rise  of  valves  for  given  pressures  when 
blowing  off,  and  maintaining  the  boiler-pressure  constant,  was 
determined  by  Mr.  Burg,  of  Yienna,  experimentally,  with  an 
ordinary  four-inch  valve.  He  found  the  rise  of  the  valve,  in 
parts  of  an  inch,  to  be  as  stated  below  for  the  various  boiler- 
pressures  given : 

For  boiler-pressures  of 

12  20          35  45  50  TO  90 

the  rise  of  the  valve  in  parts  of  an  inch  was 

JL  JL  JL  1111 

36  48  54  65"          "86  168        .168 

These  quantities  multiplied  by  the  cosine  of  the  angle  of  the 
bevel  of  the  cone  will  give  the  values  of  1,  as  experimentally 
determined. 

Employing  these  quantities,  we  may  determine  the  circum- 
ference or  diameter  d  of  a  valve  for  the  discharge  of  any  given 
quantity  of  steam  at  a  given  pressure. 

EXAMPLE. 

Taking  the  example  just  given  of  a  boiler  which  evaporates 
1,800  Ibs.  of  water  an  hour,  or  0.5  of  a  Ib.  per  second,  the  required 
area  of  discharge  was  found  to  be,  for  4  atmospheres,  0.60  of  a 
square  inch. 

Taking  1,  from  Burg's  experiments,  equal  to  -^  for  a  pressure 
of  4  atmospheres,  and  estimating  the  diameter  to  be  approxi- 
mately %  of  c,  the  circumference,  we  shall  have 

o  =  0.60  =  3  d  ^ 
d  =  16  inches 

For  a  given  area  of  disk  terminating  a  cylindrical  tube,  it  is 


198  BOILER  EXPLOSIONS. 

evident,  from  geometrical  principles,  that  to  obtain  an  orifice 
around  the  edges  of  the  valve  equivalent  to  the  cross-section 
of  the  tube,  the  valve  must  rise  for  conical  seats  more  than  J  of 
the  diameter  of  the  tube. 

The  above  analysis  of  the  action  of  the  ordinary  safety-valve 
is  given  merely  to  show  the  general  principles  on  which  this 
action  depends  to  cause  it  to  serve  as  an  automatic  regulator  of 
the  pressure ;  and  the  results  seem  to  indicate  that  in  practice 
conical  valves  are  made  too  small.  There  would  seem  to  be 
increased  safety  at  least  in  making  them  uniformly  larger. 

The  practical  conclusion  to  be  drawn  is,  that  the  ordinary 
conical  safety-valve,  considered  as  a  regulator  of  pressure,  is  too 
complicated  in  its  action,  and  too  much  influenced  by  friction 
and  other  causes,  which  cannot  be  subjected  to  ordinary  rules 
of  construction,  to  be  relied  on  exclusively  as  a  perfect  safety 
regulator,  i.e.,  as  an  automatic  means  of  keeping  the  boiler- 
pressure  constantly  at  a  given  point.  The  steam-gauge  is  in 
reality  the  main  reliance  of  the  engineer.  By  the  indications 
of  the  steam-gauge  he  can  regulate  the  pressure  through  other 
means  than  the  safety-valve,  or,  if  necessary,  can  raise  this  valve 
by  hand  when  it  is  desirable  to  keep  up  at  the  same  time  the 
rate  of  evaporation. 

261.  Sudden  Evofoition  of  Steam. — There  are  supposed  to  be, 
under  some  circumstances,  sudden  evolutions  of  steam  in  such 
quantities  that  no  relief  is  possible  through  the  medium  of 
safety-valves,  however  perfect  they  may  be  in  their  action,  and 
under  circumstances  in  which  no  warning  occurs. 

One  cause  which  has  received  the  most  general  acceptance, 
both  in  theory  and  practice,  is  the  sudden  flow  of  water  upon 
plates  which  have  become  overheated  by  the  accidental  lowering 
of  the  water-level  in  the  boiler.  There  is  no  doubt  that  the 
exposure  of  the  upper  surfaces  of  flues,  or  the  crown  of  a  furnace, 
to  intense  heat,  when  there  is  no  water  upon  these  surfaces  to 
absorb  this  heat,  is  highly  injurious  and  destructive.  The  weak- 
ening of  the  plates  under  such  circumstances  may  cause  rupture 
under  ordinary  pressures.  An  increase  of  pressure  to  a  dan- 
gerous degree  need  not  necessarily  follow,  however,  from  such 
increased  evaporation. 

Let  it  be  supposed,  for  instance,  that  ten  square  feet  of  the 
iron  of  the  flues,  J  of  an  inch  thick,  become  heated  to  1000°  F., 
and  water  already  heated  to  the  boiling-point  due  to  the  pressure, 


BOILER  EXPLOSIONS.  199 

say  300°  F.,  to  flow  over  these  plates  ;  the  cooling  of  the  plates 
from  1000°  to  300°  F.  will  cause  a  transfer  of  heat  to  the 
water  of 

Q  =  w  x  c'  x  (tj  —  t)  units  of  heat 
or  Q  =  100  Ibs.  x  ,  1138  x  700  =  7900  units 

sufficient  to  evaporate  only  about  7.9  Ibs.  of  water. 

If  the  circulation  of  the  water  is  such  that  this  quantity  of 
heat  is  equally  diffused,  the  quantity  of  heat  evolved  would  not 
elevate  the  pressure  to  a  dangerous  degree  in  the  case  given, 
under  ordinary  circumstances. 

The  effect  of  overheated  plates  in  superheating  steam  already 
formed  may  be  found  thus  :  Let  w  be  the  weight  of  steam,  c'  its 
specific  heat  at  constant  volume  =  .475  ;  then, 

Q  =  W  C'   (t,  -  t) 

and  PJ  v  =  K  TJ 

p  V  =  E  T 

p,  being  the  dangerous  pressure,  p  the  working  pressure,  t, 
and  t  being  the  corresponding  temperatures,  arid  v  the  specific 
volume,  supposed  constant. 
From  these  equations  we  get    . 


B  83.422 

in  which  the  steam  is  supposed  to  be  dry  saturated  steam. 

The  quantity  Q  may  then  be  found. 

The  evolution  of  steam  from  overheating  of  plates,  or  the 
action  of  such  plates  in  superheating  steam,  although  compara- 
tively sudden,  would  not  necessarily  be  so  sudden  as  to  prevent 
relief  through  a  perfectly  efficient  safety-valve.  The  process 
of  transfer  of  heat  in  these  cases  must,  to  a  certain  extent,  be 
gradual,  and  time  would  be  allowed  for  the  efflux  of  the  steam 
under  most  circumstances. 

A  sudden  evolution  of  steam  beneath  the  water-level  of  a  boiler, 
arising  from  any  cause,  such  as  the  "  spheroidal  condition,"  or 
concussive  "  ebullition,"  is  another  supposed  danger.  In.  this  case 
it  has  been  suggested  that  the  impact  of  a  mass  of  water  thrown 
against  opposite  plates  may  cause  rupture  ;  though  a  more 
rational  theory  seems  to  be  that  the  injury  in  such  cases  would 
arise  from  the  violent  reaction  instead  of  from  direct  impact. 
The  plates  and  joints  of  a  boiler  being  already  stretched  to  their 
extreme  limit  of  elasticity,  the  reaction  of  a  sudden  expansion 


200  BOILER  EXPLOSIONS. 

of  steam  beneath  the  water-level  might  be  transmitted  by  hy- 
drostatic pressure  over  a  large  area,  and  have  the  same  effect  as 
the  explosion  of  a  charge  of  gunpowder  upon  a  submerged  rock. 
The  whole  subject  of  sudden  evolutions  of  steam  requires, 
perhaps,  more  than  any  other,  careful  and  proper  experiments 
to  determine  the  character  and  extent  of  the  danger  which  may 
arise  from  this  cause,  or  whether  it  occurs  at  all.  Free  and 
continued  circulation  of  water,  even  if  it  be  accomplished  by  a 
forced  operation,  would  probably  be  advantageous  in  diminish- 
ing the  liability  to  sudden  evolutions  of  steam,  while  it  would  at 
the  same  time  increase  the  efficiency  of  the  heating-surfaces  at  a 
comparatively  small  cost. 


APPENDIX   A. 


THE  law  known  as  Mariettas  law,  and  also  as  Boyle's  law  (discovered  by 
Mariotte  in  1740),  is  a  simple  law  in  regard  to  perfect  gases,  determined 
by  experiment,  which  may  be  enunciated  as  follows:  "The  temperature 
of  the  gas  remaining  constant,  the  volumes  of  the  same  weight  at  different 

Y)  V* 

pressures  will  be  inversely  as  the  pressures."     Thus  p  v  =  p'  v'  or  -/=  _. 

If  densities  be  considered,  the  volumes  being  inversely  as  the  densities, 
the  law  may  be  stated  in  other  words  ;  thus,  "  at  the  same  temperature,  the 
densities  of  a  given  quantity  of  a  perfect  gas  occupying  different  volumes 

1  1         p        D 

will  be  proportional  to  the  pressures.    Thus  p  -  =  p'  ^-  or  —,  =  ~  . 

The  experiments  of  Gay-Lussac  on  the  expansion  of  gases,  with  constant 
pressure,  led  him  to  the  discovery  that  "  the  augmentation  of  volume 
which  a  perfect  gas  receives  when  the  temperature  is  increased  1°,  is  a 
fixed  proportion  of  its  initial  volume  at  the  temperature  of  melting  ice  ;  or 
v'  —  v0  (1  +  a  t),  in  which  (a)  is  a  coefficient  of  expansion,  nearly  the 
same  for  all  perfect  gases.  Combining  this  discovery  with  the  law  of 

Mariotte,  the  relation  --    =  —  (  ---         -  Y  known  as  the  law  of  Mariotte 
Vo         p   \l  "*~  a  to/ 

and  Gay-Lussac,  is  determined.  From  this  relation  is  easily  derived  the 
general  form  p  v  =  R  (a  +  t)  or  p  v  =  R  T,  which  occurs  in  the  text  (see 
page  25). 

Poisson  discovered  that  when,  during  the  expansion  or  compression  of 
a  gas,  no  heat  is  transmitted  to,  or  abstracted  from,  the  gas  (the  cooling  or 
heating  due  to  the  work  involved  being  thus  confined  to  the  gas  itself), 
the  law  which  expresses  the  relation  between  the  pressure  and  volume  will 
take  the  form,  algebraically, 

k  k 

p  v     =  pi  vi     =  a  constant. 

From  this  equation  we  have  directly 


V 

or  since  p  v  =  B,  T  and  pi  Vi  =  R  TI 


and  the  other  equations  of  page  33  are  found  in  the  same  manner. 


202  APPENDIX  A. 

The  equation  p  v  =  R  T,  when  T  is  constant,  is  the  equation  of  an  equi- 
lateral hyperbola,  which  is  the  curve  of  expansion  of  a  perfect  gas  when 
the  temperature  is  kept  constant  by  a  supply  of  heat  to  the  gas  equivalent 

k  k 

to  the  work  of  expansion.     The  equation  p  v      =  pi  Vj      —    constant  is 

the  equation  of  a  curve  of  expansion,  called  the  adiabatic  curve,  which  is 
the  curve  representing  the  relations  of  the  pressure  and  volume  when  a  gas 
expands  against  a  pressure,  the  heat  which  is  converted  into  work  being 
drawn  from  the  gas  itself.  The  expression  for  the  work  performed  under 
such  conditions  is  given  page  33  in  terms  of  the  initial  and  final  volumes. 
A  corresponding  expression  for  the  work  in  terms  of  the  initial  and  final 
pressures,  is — 

1  I  /  TV,   \ 

w=  — 


The  value  of  k  for  wet  steam  is  1.105  (0.7  by  weight  being  steam,  and 
0.3  water).  For  'dry  steam  k  =  1.135,  for  superheated  steam  k  =  1.333, 
and  for  air  k  =  1.41. 


I.'NIVKUSITV 


APPENDIX   B. 


THE  following  are  Professor  Zeuner's  formulae  for  the  flow  of  vapors 
and  gases  from  orifices,  to  which  tables  of  coefficients  have  been  added, 
calculated  from  these  formulas  for  convenience  of  calculation. 

On  page  157  and  on  page  402  of  Professor  Zeuner's  work  on  the  Dyna- 
mic Theory  of  Heat,  French  edition,  we  have  the  equation — 


w  representing  the  velocity  of  efflux  ;  v  the  specific  volume  ;  and  p  the 
pressure.     Assuming  that  the  form  of  the  adiabatic  curve  for  vapors  is  the 

k 
same  as  for  gases,  viz.  :  p  v     =  constant,  (2)  we  can,  by  finding  the  value 

of  v  in  equation  (2)  and  substituting  in  equation  (1),  get 


a  formula  first  deduced  by  Weisbach,  which  is  true  for  any  gas  or  vapor 

j, 

'that  has  for  the  equation  of  its  adiabatic  the  form  p  v  =  constant.  The 
different  values  of  k  for  steam  in  different  conditions,  and  for  air,  are 
given  on  the  preceding  page. 

Equation  (3)  is  also  identical  with  equation  (337),  page  406  (Zeuner), 
from  which  he  calculated  the  values  of  w  on  page  409. 

Equation  (3)  is  best  adapted  for  discussion,  and  will  therefore  be  em- 
ployed instead  of  (337). 

Equation  (3)  can  be  changed  into  the  following  forms  : 


(4)    w  = 


(5)    w  = 


204:  APPENDIX  B. 

From  equation  (331),  page  403  (Zeuner),  we  get 


(6)  * 

F  Vj 

k  k 

Substituting  in  (6)  eq.  3  and  4,  and  remembering  that  p2  v2      —  pi  Vi 

Vi  =    (  V—  )  JT  ,  we  get  equations  (7)  and  (8). 
^Pi  / 


p 

(?)      £  = 


Equations  4,  5,  7,  and  8  are  theoretical  equations  in  which  friction  is 
neglected,  and  in  which  F  represents  that  section  of  the  stream  in  which 
there  exists  the  external  pressure  p1?  and  hence  FI  may  be  variable.  The 
section  just  mentioned  is  called  by  Professor  Zeuner  the  efflux  section  to 
distinguish  it  from  the  orifice  section.  Kankine  calls  it  the  effective  area. 

G  is  suppdsed  to  be  known  and  constant. 

Equation  (3)  was  deduced  by  supposing  that  while  the  fluid  is  expand- 
ing from  the  boiler  into  the  external  space,  heat  is  neither  furnished  nor 
abstracted ;  but  this  is  not  exactly  the  case  in  practice,  because  the  fluid  on 
its  way  to  and  at  the  orifice  gives  rise  to  friction,  which  in  turn  produces 
heat ;  so  that,  strictly  speaking,  heat  is  furnished  to  the  fluid  in  an 
amount  almost  equivalent  to  the  friction  (an  insignificant  quantity  of  heat 
being  lost  by  conduction).  So  that  the  true  curve  of  expansion  is  not 
the  adiabatic  curve,  but  one  which  will  take  a  position  above  the  latter, 

and  which  Zeuner  shows  for  gas  to  have  the  form  (p  v  n  =  const.)  (9) 
in  which 

(1  +  z)  k 


(10)    n  = 


1  +  zk 


This  n  Professor  Zeuner  calls  the  coefficient  of  efflux.  Its  value  evidently 
depends  on  z  and  k.  z  is  a  coefficient  of  resistance,  and  is  equal  to  the 
ratio  of  the  actual  (not  theoretical)  living  force  to  the  resistances  of  the  is- 
suing fluid,  i.e.,  arising  from  friction  and  oscillations. 

* 
z  _  Friction 


Actual  Living  Force 

It  is  only  apparently  like  Weisbach's  coefficient,  and  is  to  be  determined 
by  experiment. 

k  is  the  exponent  in  the  equation  of  the  adiabatic  curve.     By  combining 


APPENDIX  B.  205 

equations  9,  6,  and  3  in  the  same  way  as  6,  3,  and  2,  we  get  equations 
similar  to  8,  7,  5,  and  4. 


(11)    w  = 


(12)     w  = 


(13)     ^-  = 


n  +  1 
(14) 


-. 


Equations  4,  5,  11,  and  12  give  the  velocity  of  the  particles  in  feet  or 
metres  per  second.  Equations  7,  8,  13,  and  14  give  the  quantity  of  fluid 
which  flows  through  unit  of  area,  in  pounds  or  kilograms,  per  second. 
This  last  Rankine  calls  mass  velocity.  In  equations  13  and  14  it  must  be 
remembered  that  FI  still  represents  the  efflux  section  of  the  stream,  and  pi 
the  pressure  in  that  section. 

It  can  easily  be  shown  by  analyzing  equations  4,  5, 11,  and  12  that  both 
when  there  is  friction  and  when  there  is  no  friction,  the  velocity  w  in  the 
efflux  section  never  attains  a  maximum,  but  depends  entirely  on  the  differ- 
ence of  pressures  in  the  boiler  and  in  the  external  space. 

Equations  8  and  14,  however,  show  that  there  is  a  maximum  mass  velocity 
when 

k 

(15)      Pl    _  (     2       ^-^  (theoretically),  and 
p2    ~~  \k  + 


(16)     .£.=: 

P2 


n 
n^Ti  (actual) 


Napier's  experiments  go  to  show  that  when  there  is  a  constant  inside 
pressure  and  a  variable  outside  pressure,  there  is  a  certain  ratio  between 

"W 

these  two  pressures  when  both  the  velocity  w  and  the  —  in  the  plane  of  the 

actual  orifice  attain  a  maximum.      His  experiments  also  show  that  if  the 
external  pressure  (not  that  in  the  actual  orifice)  falls  below  that  value 


206  APPENDIX  B. 

which  gives  a  maximum,  the  pressure  in  the  plane  of  the  actual  orifice  will 
remain  constant,  even  if  the  external  pressure  should  become  0.     When 
n  n 

.PL  =  (_*_V-  !  or  S  greater  than  /    2 
pa    "    \n  +  I/  Vn  +  I 

the  pressure  in  the  plane  of  the  orifice  is  equal  to  the  external  pressure. 
But  when 

n 


—  is  less  than  ( 

Pa  \n  +  1. 

the  pressure  p  in  the  plane  of  the  actual  orifice  is  given  by  the  equation 


p=p°GJh)11 


-1 


Independent,  therefore,  of  the  external  pressure,  experiment  and  theory 
both  seem  to  show  that  when  there  is  a  constant  inside  pressure  and  a 
variable  external  pressure,  the  pressure  in  the  plane  of  the  orifice  can 
never  fall  below  the  value  given  in  equation  18,  i.e.,  the  value  corre- 
sponding to  a  maximum  efflux.  It  may  go  above  that  value,  but  never 
below. 

If  it  be  desired  to  find  an  orifice  that  will  discharge  a  given  weight  G  in 
a  unit  of  time,  the  pressure  in  the  reservoir  being  constant,  and  equal  to 
p2,  and  the  external  pressure  in  the  receiver  being  pi,  the  process  will  be  as 
follows : 

First,  find  the  pressure  in  the  plane  of  the  actual  orifice;  this  will  be 
the  same  as  the  actual  pressure  pi  if  pi  is  equal  to,  or  greater  than, 
n 

p2  f  — — -z  ln  ~~    .     But  if  P!  is  less  than  this  quantity,  then  the  pressure  p 
in  the  plane  of  the  orifice  will  be 


Then  substitute  one  or  the  other  of  these  values  in  equation  (14),  and 
regard  F!  as  being  the  actual  orifice,  which  may  then  be  called  F.  n  can  be 
obtained  from  equation  (10)  or  from  the  following  tables. 

Rankine  gives  the  following  rough  formulae  for  finding  the  efflux  of 
steam,  which  are  intended  to  be  sufficiently  accurate  for  practical  pur- 


In  the  first  case,  when  pa  =  or  greater  than  -  pi,  then, 

3 


2  —   P? 

p  ~~  70 


PI  and  pa  being  absolute  pressures. 


APPENDIX  B.  207 


In  the  second  case,  when  p2  is  less  than  _  plt 

3 


_^___Pl_     ,     /  JL       P2  —  Pl 

P  ~~  42    V    2         p2 


Napier's  formulae  are  — 

First,  when  p2  is  greater  than  2  pj? 


Second,  when  p2  is  less  than  2  pt 


P2  /  V2 

In  these  formulae  F  represents  the  actual  orifice,  and  G  the  weight  of  steam 
discharged  per  second. 

n 

When  pi  is  less  than  pa  (     2     \n  —  1  (which  is  true  for  steam  in  all  cases 

\n  +  I/ 

in  which  p2  is  greater  than  1.726  pi),  then  the  pressure  p  in  the  plane  of 

n 

the  orifice  becomes  p  =  p2  (     n     p  —  1,  and  this  introduced  into  equa- 

\n  +  I/ 
tion  14  gives 

G        /    2     \  -  -      f~      k      /n  —  1\    pa 

F  =  (^ri>  -  l  V  2g  k^i  (n-n)  ^ 

Supposing  the  resistances  constant,  this  is  equivalent  to 


a  form  corresponding  to  that  found  by  Napier  from  experiment. 


208 


APPENDIX  B. 


TABLE   I.* 

Showing  the  ratio  of  the  actual  orifice  to  the  tJieoretical  orifice  . —  in  the  efflux 

F\ 

of  wet  and  dry  steam,  the  value  of  F  being  found  from  equations  7  and  8, 
friction  being  neglected;  the  value  of  Ft  being  found  from  equations  13  and 
14,  friction  being  taken  into  account. 


Absol. 
press. 
in 

atmos. 

Wet  Steam. 

Dry  Steam. 

z  =  0.065 

z  =  0.100 

z  =  0.505 

z  =  0.9601 

z  =  0.065 

z  =  0.100 

z  =  0.505 

z=  0.9601 

1.25 
1.50 
1.714 
1.732 

1.856 
1.90U 
2.000 
4.00 
7.00 
10.000 
14.000 
k 
n 

1.03171 
1  .0333 

1.0449 
1.0504 

1.2360 
1.2421 

1.4119 

1.4207 

1.0344 

1.0522 

1.2420 

1.4279 

1.0357 

1.0542 

1.2474 

1.4393 

"'i'.4i79' 
1.06710 
0  75983 
0.59759 
0.46464 
1.135 
1.0646 

1.0169 
0.7535 
0.53262 
0.41593 
0.32588 
1.105 
1.0(.)8 

1.0344 
0.76835 
0.54054 
0.42309 
0.33149 
1.105 
1.0946 

1.2211 
0.90699 
0.63955 
0.49943 
0.39130 
1.105 
1.0675 

1.4038 
1.0428 
0.72686 
0.57419 
0.44987 
1.105 
1.0509 

1.0203 
0.76792 
0.54678 
0.4303 
0.33867 
1.135 
1.1257 

1.0385 
0.78164 
0.55655 
0.43771 
0.34432 
1.135 
1.1212 

1.22903 
0.92427 
0.64166 
0.50465 
0.39697 
1.135 
1.0858 

In  the  wet  steam,  0.7  by  weight  is  suppposed  to  be  steam  and  0.3  water, 
k  =  1.105  is  the  exponent  of  the  adiabatic  curve  of  the  fluid,  z  is  a  coeffi- 
cient of  resistance  due  to  friction  =  the  ratio  of  friction  to  actual  living 
Friction  (1  +  z)  k 

force  =  0* the  lssuing  fluid'    n  =  '  and 


to  the  theoretical in  the 


hence  less  than  k. 

TABLE  II.* 

Showing  the  ratio  of  iJie  actual  orifice  of 

JJ  ] 

efflux  4>f  superheated  steam  and  air  ;  the  value  of  F  being  found  by  equa- 
tions 7  and  8,  friction  being  neglected ;  F^  being  found  from  equations  13 
and  14,  friction  being  taken  into  account. 


Absol. 
press, 
in 
atmos. 

Superheated  Steam. 

Air. 

z  =  0.065 

z  =  O.lOOJz  =  0.505 

i 

z  =  0.9601 

z  =  0.065 

z  =  9.100 

z  =  0.605 

z  =  0.9601 

1.856 
1.800 
2.000 
4.000 
7.000 
10.000 
14.000 
k 
n 

1.0393 

1.0599 

1.27375 

1.4194 

1.0423 
1.0414 
0.85885 
f.  65914 
0.54397 
0.44899 
1.41 
1.3754 

1.0624 
1  .0615 
0.87539 
0.67183 
0.55445 
0.45763 
1.41 
1.3593 

Vi  .2832 
1.2821 
1.0573 
0.8114 
0.6K967 
0.55273 
1.41 
1.2395 

1.5014 
1.4949 
1.2370 
O.U4SM 
0.78354 
0.6467 
1.41 
1.174 

1.0355 
0  88547 
0.62975 
0  .51369 
0.41929 
1.3333 
1.30675 

i  .osei 

0.85206 
0.64211 
0.52287 
0.42761 
1.3333 
1.2941 

1  2691 
1.02400 
0.77180 
0  62960 
0.51390 
1.333 
1.1992 

1.4144 
1.14110 
0,86003 
0.70155 
0.57265 
1.888 
1.1460 

*  Calculated  from  the  foregoing  formulae,  by  Mr.  J.  F.  Klein. 


APPENDIX  B. 


209 


In  the  wet  steam,  0.7  by  weight  is  supposed  to  be  steam,  and  0.3  water. 

k  =  1.105  is  the  exponent  of  the  adiabatic  curve  of  the  fluid  p  v  =  const, 
z  is  a  coefficient  of  resistance  equal  to  the  ratio  of  friction  to  the  actual 
(not  theoretical)  living  force  of  the  issuing  fluid.  When  friction  is  taken 
into  account  the  adiabatic  curve  changes  to  the  curve  represented  by 

p  v  n  =  const,  in  which  n  =  J -2_    and  hence  less  than  k. 

1  +    z  k 

According  to  a  principle  of  hydraulics,  z  is  assumed  by  Professor  Zeuner 
to  be  constant  for  the  same  kind  of  tube  and  orifice  of  discharge,  how- 
ever the  diameter  of  orifice,  or  the  pressure,  may  vary.  This  is  allow- 
able when  the  tubes  which  form  the  orifice  are  rounded  on  the  inner 


From  equation  (3)  or  an  identical  equation  Prof.  Zeuner  has  calculated 
( Theorie  de  la  Chaleur)  the  velocities  of  steam  issuing  from  an  orifice  in  a 
boiler,  and  from  these  the  quantity  of  flow  per  unit  of  effective  or  theoreti- 
cal area,  for  different  absolute  pressures.  The  velocities  are  as  given 
below : 


Internal  absolute  pressures. 
Atmospheres. 

Velocities  in  metres  per 
second. 

Flow  of  steam  per  second,  in 
pounds,  per  square  inch  of  section. 

1    . 

2  
3 

481.72  
..    .606  62 

0.434 
.    ..             0  559 

4  

681  56 

0  639 

5  
6  
7  

734.42   
775.00  
807  82         

0.698 
..0.744 
0  .  783 

8  
9  

835.00  
858.41  

0.815 
0.845 

10  

878.92  . 

0  869 

11  
12  

896.87  
913.05         

0.892 
0  911 

To  use  this  table,  let  it  be  required  to  find  an  orifice  which  will  discharge 
a  given  weight,  w,  of  dry  steam  per  second  at  a  given  pressure  ;  for  in- 
stance, the  orifice  that  will  discharge  1,800  pounds  per  hour,  or  0.5  pounds 
per  second,  at  four  atmospheres. 

In  the  third  column  we  find  the  weight  discharged  per  square  inch  per 

second,  viz.  :  0.  639  pounds,  then    ^—  =  A,  the  theoretical  orifice,  or  ori- 

.639 


w 


-  -783.     Then  find  the  proper 


fice  in  the  effective  section  ; 

coefficient  for  4  atmospheres  from  the  tables,  viz.  :  .768,  and  .783  X  .768  = 
0.60  square  inch.  For  superheated  steam  and  air  the  process  is  similar 
after  finding  the  flow  per  square  inch  per  second  from  the  theoretical 
formula. 

14 


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governors,  and  many  standard  and  novel  examples,  mostly  from 
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A  FEW  FROM  MANY  TESTIMONIALS. 

*  It  seems  to  me  that  your  Works  only  need  a  thorough  examination  to  be  intro- 
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I ...  —Prof.  J.  G.  FOX,  Collegiate  and  Engineering  Institute,  Kew  York  City. 

44 1  have  used  several  of  your  Elementary  Works,  and  believe  them  to  be  better 
adapted  to  the  purposes  of  instruction  than  any  others  with  which  I  am 
acquainted."— H.  F.  WALLING,  Prof,  of  Civil  and  Topographical  Engi- 
neering, Lafayette  College,  Easton,  Pa. 

**Your  Works  appear  to  me  to  fill  a  very  important  gap  in  the  literature  of  the 
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and  meets  my  heartiest  approval.  This  is  the  distinguishing  feature  <jt  your 
Elementary  Works."— Prof.  H.  L.  EUSTIS,  Lawrence  Scientific  School, 
Cambridge,  Mass. 

"The  author  has  happily  divided  the  subjects  into  two  great  portions :  the  foimer 
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COMBINATION,  AND  APPLICATION  OF  CALCA- 
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MAHAN  MECHANICAL     PRINCIPLES     OF     ENGINEERING 

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From  last  London  edition,  with   considerable  additions,  by 

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WOOD.  A    TREATISE    ON    THE    RESISTANCE    OF    MATE- 

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it  appears — that  is  to  say,  every  occurrent  person,  number, 
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word  can  perplex  the  beginner,  but,  assured  of  the  precise 
«  grammatical  force  of  any  word  he  may  desire  to  interpret,  he 

is  able  immediately  to  apply  his  knowledge  of  the  English 
meaning  of  the  root  with  accuracy  and  satisfaction.     1  vol. 

small  4to,  half  bound $6  50 

*  GREEK-ENGLISH  LEXICON  TO  TESTAMENT.  By 
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HEBREW. 

GREEN.  A  GRAMMAR  OF  THE  HEBREW  LANGUAGE.     With 

copious  Appendixes.      By  W.  H.  Green,  D.D.,  Professor  irj 

Princeton  Theological  Seminary.     1  vol.  8vo,  cloth. . .  .$3  50 

"  AN     ELEMENTARY    HEBREW    GRAMMAR.       With 

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**  HEBREW  CHRESTOMATHY;  or.  Lessons  in  Readivu-  and 
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cloth $2  00 

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JOHN   WILEY    &   SON'S   LIST    OF   PUBLICATIONS, 


99 


BACSTER'S          BAGSTER'S    COMPLETE    EDITION    OF    GESENIUS 
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clear,  and  perfect  type.     Translated  and  edited  with  addi- 
tions and  corrections,  by  S.  P.  Tregelles,  LL.D. 
In  this  edition  great  care  has  been  taken  to  guard  the  student  from  Neologiaa 

tendencies  by  suitable  remarks  whenever  needed. 

"The  careful  revisal  to  which  the  Lexicon  has  been  subjected  by  a  faithful  and 
Orthodox  translator  exceedingly  enhances  the  practical  value  of  this  edition." 
— Edinburgh  Ecclesiastical  Journal. 

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BACSTER'S          NEW  POCKET  HEBREW  AND  ENGLISH  LEXICON. 

The  arrangement  of  this  Manual  Lexicon  combines  two 
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order  of  words.  This  arrangement  tends  to  lead  the  learner 
onward;  for,  as  he  becomes  more  at  home  with  roots  and 
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IRON,  METALLURGY,  &c. 

BOBEMANN.  A  TREATISE  ON  THE  ASSAYING  OF  LEAD,  SILVER, 
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Kerl.  Translated  b/  W.  A.  Goodyear.  1  vol.  12mo,  $2  50 

CROOKES.  A  PRACTICAL  TREATISE  ON  METALLURGY.    Adap- 

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8vo.     Price $30  00 

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and  Sulphur $10  00 

Vol.  2.  Copper  and  Iron 10  00 

Vol.  3.   Steel,  Fuel,  and  Supplement 10  00 

DUN  LAP.  WILEY'S  AMERICAN  IRON  TRADE  MANUAL  of  the 

leading  Iron  Industries  of  the  United  States.  With  a 
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HOLLY.  SAW  FILING.  The  Art  of  Saw  Filing  Scientifically  Treated 
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.KNIGHT,  THE  MECHANISM  AND   ENGINEER  INSTRUCTOR, 

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100  JOHN   WILEY   &    SON'S    LIST    OF    PUBLICATIONS. 

TURNING,  &c.  LATHE,  THE,  AND  ITS  USES,  ETC.;  or,  Instruction  ic 
the  Art  of  Turning  Wood  and  Metal.  Including  a  descrip- 
tion of  the  most  modern  appliances  for  the  ornamentation  of 
plane  and  curved  surfaces,  with  a  description  also  of  an 
entirely  novel  form  of  Lathe  for  Eccentric  and  Rose  Engine 
Turning,  a  Lathe  and  Turning  Machine  combined,  and  other 
valuable  matter  relating  to  the  Art.  1  vol.  8vo,  copiously 
illustrated.  Including  Supplement.  8vo,  cloth $7  00 

"  The  most  complete  work  on  the  subject  ever  published."— American  Artisan. 

"Here  is  an  invaluable  book  to  the  practical  workman  and  amateur." — London 
Weekly  Times. 

TURNING,  &c.  SUPPLEMENT  AND  INDEX  TO  LATHE  AND  ITS 
USES.  Large  type.  Paper,  8vo $090 

WILLIS.  PRINCIPLES  OF  MECHANISM.     Designed  for  the  use  of 

Students  in  the  Universities  and  for  Engineering  Students 
generally.  By  Robert  Willis,  M.D.,  F.R.S.,  President  of  the 
British  Association  for  the  Advancement  of  Science.  &c.,  &c. 
Second  edition,  enlarged.  1  vol.  8vo,  cloth $7  50 

*$*  It  ought  to  be  in  every  large  Machine  Workshop  Office,  in  every  School  of 
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MANUFACTURES. 

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MAKERS'  MANUAL.  Comprising  descriptions  of  the 
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use  in  French,  Swiss,  and  English  clocks  and  watches,  Patents, 
Tools,  etc. ,  with  directions  for  cleaning  and  repairing.  With 
numerous  engravings.  Compiled  from  the  French,  with  an 
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America.  By  Mary  L.  Booth.  With  numerous  plates.  1 
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CELDARD.  HANDBOOK    ON    COTTON    MANUFACTURE;     or,    A 

Guide    to    Machine-Building,    Spinning,    and    Weaving. 

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useful  and  important  tables.  The  whole  intended  to  be  a 
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cotton.  By  James  Geldard.  With  steel  engravings.  1  voL 
12mo,  cloth $2  50 

MEDICAL,  &c. 

BULL.  HINTS  TO  MOTHERS  FOR  THE  MANAGEMENT  OF 
HEALTH  DURING  THE  PERIOD  OF  PREG- 
NANCY, AND  IN  THE  LYING-IN  ROOM.  With  an 
exposure  of  popular  errors  in  connection  with  those  subjects. 
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FRANCKE  OUTLINES  OF  A  NEW  THEORY  OF  DISEASE,  applied 

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a  critique  on  Priessnitz's  mode  of  treatment.  Intended  foi 
popular  use.  By  the  late  H.  Francke.  Translated  from  the 
German  by  Robert  Blakie,  M.D.  1  vol.  12mo,  cloth. .  .$1  50 

GREEN.  A  TREATISE  ON  DISEASES  OF  THE  AIR  PASSAGES. 

Comprising  an  inquiry  into  the  History,  Pathology,  Causes, 
and  Treatment  of  those  Affections  of  the  Throat  called  Bron 
chitis,  Chronic  Laryngitis,  Clergyman's  Sore  Throat,  etc. ,  etc. 
By  Horace  Green,  M.  D.  Fourth  edition ,  revised  and  enlarged 
1  vol.  8vo,  cloth $3  06 

««  A  PRACTICAL  TREATISE  ON  PULMONARY  TUBER. 
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doth. $5  OC 


JOHN    WILEY   &    SON"S   LIST    OF    PUBLICATIONS. 


10\ 


CREENi,  OBSERVATIONS  ON  THE   PATHOLOGY  OF  CROUP 

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ON  THE  SURGICAL  TREATMENT  OF  POLYPI  OF 
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TILT.  ON    THE    PRESERVATION    OF    THE    HEALTH    OF 

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VON  LHJBEN.  GUSTAF  VON  DUBEN'S  TREATISE  ON  MICRO- 
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MINERALOGY. 

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Cloth $  1 0  00 

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ration. ) 

MISCELLANEOUS. 
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CARLYLE.  ON  HEROES,  HERO-WORSHIP,  AND  THE  HEROIC  IN 

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102 


JOHN   WILEY    &    SON'S   LIST    OF   PUBLICATIONS. 


EDWARDS.  FREE  TOWN  LIBRARIES.     The  Formation, 

and  History  in  Britain,  France,  Germany,  and  America. 
Together  with  brief  notices  of  book-collectors,  and  of  the 
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GREEN.  THE  PENTATEUCH  VINDICATED  FROM  THE  AS- 
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COURAUD.  PHRENO-MNEMOTECHNY;    or,    The    Art    of  Memory. 

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44  FHRENO-MNEMOTECHNIC  DICTIONARY.  Being  a 
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"  CATALOGUE  OF  AMERICAN  BOOKS.  The  American 
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MAVER'S  COLLECTION  OF  GENUINE   SCOTTISH  MELODIES. 

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NOTLEY.  A  COMPARATIVE  GRAMMAR  OF  THE  FRENCH, 
ITALIAN,  SPANISH,  AND  PORTUGUESE  LAN- 
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Svota,.  .I $4  00 


JOHN    WILEY    &    SON'S    LIST    O*    PUBLICATIONS.  103 

RUSKIN'S     WORKS. 

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